How Did the First Atom Form? Where did it come from? | Big Bang Nucleosynthesis

Complex Science Explained Simply
21 Nov 202116:46

Summary

TLDRThis video script delves into the origins of atoms and the universe, explaining the Big Bang as a period of rapid expansion, not a singular starting point. It outlines the timeline of the universe's early moments, from the Planck epoch to inflation, and discusses the formation of fundamental particles, the quark epoch, and the emergence of stable atoms. The script also touches on the mystery of matter-antimatter asymmetry and the cosmic microwave background, setting the stage for the exploration of heavier elements' creation in a subsequent video.

Takeaways

  • 🌌 The universe is composed of an immense number of atoms, estimated to be more than 10^78.
  • 🔬 Atoms are made up of subatomic particles: electrons, protons, and neutrons, which are themselves composed of quarks.
  • 💥 The origin of the particles that make up atoms is believed to be the Big Bang, where immense energy condensed to form atoms.
  • ⏳ The Big Bang theory is not about the exact moment the universe began but rather the period of rapid expansion and high density that followed.
  • 🚫 Our understanding of the universe's beginning is limited by incomplete theories that break down near the 'singularity' at t=0.
  • 🕒 The Planck epoch, around 10^-43 seconds after the Big Bang, is the earliest period we can theoretically understand, requiring a quantum theory of gravity.
  • 🔄 The universe underwent a phase of inflation, expanding exponentially faster than the speed of light, which is not a violation of causality.
  • 🌀 The forces of nature, including gravity, are thought to have unified into a single force during the Planck epoch and then separated as the universe expanded.
  • 🌡 The universe transitioned from a quark-gluon plasma to a hadron gas as it cooled, leading to the formation of protons, neutrons, and electrons.
  • 💥 A matter-antimatter asymmetry resulted in a slight excess of particles over antiparticles, allowing for the formation of stable atoms.
  • 🌟 The cosmic microwave background (CMB) is the residual radiation from the time when the universe became transparent as electrons combined with nucleons to form neutral atoms.

Q & A

  • What is the estimated number of atoms in the observable universe?

    -There are estimated to be more than ten quadrillion vigintillion atoms in the observable universe, which is 1 followed by 78 zeros.

  • What are the basic components of an atom?

    -Atoms are made up of electrons, protons, and neutrons, which in turn are composed of quarks.

  • What is the short answer to where the particles that make up atoms came from?

    -The short answer is the Big Bang, where immense energy condensed and atoms formed.

  • What is the limitation of our current understanding of the universe's beginning?

    -Our current theories are incomplete, and we cannot accurately describe what happened at the very beginning of time, known as the singularity.

  • What is the Planck time and why is it significant?

    -The Planck time is about 10^-43 seconds, the smallest unit of time that can theoretically exist according to quantum mechanics. It is significant because it is the closest point in time to the beginning that we can theoretically understand.

  • What is the concept of inflation in the context of the Big Bang?

    -Inflation is a theorized period from about 10^-36 to 10^-33 seconds after the Big Bang when the universe expanded exponentially faster than the speed of light.

  • Why is the Big Bang not considered as an event at t=0?

    -The Big Bang is not considered as an event at t=0 because it refers to a period in the early universe when it was very hot, dense, and expanding rapidly, rather than a specific starting point.

  • What is the significance of the electroweak symmetry breaking?

    -Electroweak symmetry breaking, occurring around 10^-11 seconds, is significant because it led to the separation of the electromagnetic and weak forces and allowed fundamental particles to gain mass through interaction with the Higgs field.

  • What is the matter-antimatter asymmetry and why is it important?

    -The matter-antimatter asymmetry refers to the imbalance between the creation of particles and antiparticles. It is important because it allowed for the existence of matter in the universe, as without it, all particles would have annihilated with antiparticles, leaving only photons and neutrinos.

  • What is the cosmic microwave background (CMB) and how is it related to the formation of the first atoms?

    -The cosmic microwave background (CMB) is the residual radiation from the Big Bang. It is related to the formation of the first atoms because it was released when the first stable neutral atoms were formed, allowing photons to travel freely through space.

  • What is the process of Big Bang nucleosynthesis and what elements were formed during this process?

    -Big Bang nucleosynthesis is the process that occurred around 17 minutes to 20 minutes after the Big Bang, during which the universe formed its first elements, primarily Hydrogen and Helium-4, along with trace amounts of deuterium, Helium-3, and Lithium-7.

Outlines

00:00

🌌 The Big Bang and the Birth of Atoms

This paragraph delves into the fundamental concepts of the universe's composition and the origins of atoms. It introduces the concept of the big bang as the starting point for the formation of atoms and explains the limitations of our current understanding of the universe's inception. The paragraph also touches upon the Planck epoch, the earliest point in time we can theoretically access, and the challenges of understanding what occurred before this. It sets the stage for the journey through the early universe's timeline, leading up to the formation of atoms.

05:01

🚀 Cosmic Inflation and the Quest for Understanding the Universe's Early Moments

The second paragraph explores the concept of cosmic inflation, a period of rapid expansion in the early universe that occurred between 10^-36 and 10^-33 seconds post-big bang. It discusses the mysteries surrounding the energy source that fueled this expansion and the information loss it caused. The paragraph also touches on the standard model of cosmology, which is well understood from around 10^-12 seconds, and the speculative nature of theories before this time. It outlines the timeline of the universe's evolution, including the separation of forces and the formation of a quark-gluon plasma, setting the stage for the emergence of mass through the Higgs field.

10:04

🔬 The Formation of Atoms and the Matter-Antimatter Asymmetry

This paragraph examines the process of atomic formation in the early universe, starting from the quark epoch and moving through the lepton epoch. It explains how the universe transitioned from a state of quarks and gluons to a hadron gas, which included protons, neutrons, and mesons. The discussion includes the annihilation of particles and antiparticles, leading to a slight excess of particles that allowed for the formation of atoms. The paragraph also highlights the mystery of matter-antimatter asymmetry and the significance of this imbalance in the creation of the first atoms.

15:06

🌟 The Cosmic Microwave Background and the Formation of Neutral Atoms

The final paragraph of the script discusses the process of recombination, where electrons finally become bound to nucleons to form neutral atoms, which occurred around 380,000 years after the big bang. It explains how this event led to the universe becoming transparent, allowing photons to travel freely and create the cosmic microwave background (CMB) that we observe today. The paragraph also hints at the continuation of the story in a subsequent video, focusing on the formation of heavier elements essential for life and introduces a sponsored course on chemical reactions available on Brilliant.

Mindmap

Keywords

💡Atoms

Atoms are the basic units of matter, composed of protons, neutrons, and electrons. In the context of the video, they are discussed as being made up of even smaller particles like quarks. The formation of atoms from these fundamental particles is central to understanding the early universe and the origins of matter, as highlighted in the script where it mentions that atoms are made from electrons, protons, and neutrons.

💡Big Bang

The Big Bang is the prevailing cosmological model that explains the origin of the universe. It suggests that the universe began as a singularity and has been expanding ever since. In the video, the Big Bang is not just a moment in time (t=0), but a period characterized by rapid expansion and high energy, which is crucial for understanding the formation of atoms and the universe's evolution.

💡Planck Time

Planck time is the smallest unit of time that can theoretically be measured, approximately 10^-43 seconds. The video mentions that our current theories become unreliable at this scale, making it a significant concept in understanding the limits of our knowledge about the early universe. It is the earliest point in time that we can theoretically discuss in the context of the Big Bang.

💡Inflation

Inflation is a theory that suggests a rapid exponential expansion of the universe during its early stages, occurring from about 10^-36 to 10^-33 seconds after the Big Bang. This concept is key to the video as it explains how the universe grew from a tiny point to a much larger size, setting the stage for the formation of atoms and the structure of the universe we observe today.

💡Electroweak Force

The electroweak force is a unified description of two of the four fundamental forces in nature: the electromagnetic force and the weak nuclear force. In the video, it is mentioned that these forces were united during the early universe and later separated, which is essential for understanding the development of fundamental particles and their interactions.

💡Higgs Field

The Higgs field is a theoretical field that permeates all of space and is responsible for giving particles mass through interaction with the Higgs boson. The video discusses how the Higgs field gains a non-zero potential, leading to the mass of fundamental particles, which is a critical step in the formation of atoms.

💡Quark-Gluon Plasma

A quark-gluon plasma is a state of matter that is thought to have existed shortly after the Big Bang, where quarks and gluons, the constituents of protons and neutrons, were free and not bound into hadrons. The video mentions this state as a precursor to the formation of hadrons like protons and neutrons, which are necessary for the creation of atoms.

💡Nucleosynthesis

Nucleosynthesis refers to the process by which atomic nuclei are formed, particularly in the context of the early universe. The video discusses Big Bang nucleosynthesis, which occurred around 20 minutes after the Big Bang, resulting in the formation of light elements like hydrogen and helium. This process is foundational to understanding the elemental composition of the universe.

💡Recombination

Recombination is the process by which electrons combine with atomic nuclei to form neutral atoms. In the video, it is described as occurring around 380,000 years after the Big Bang, when the universe cooled enough for electrons to bind to nuclei, leading to the release of photons and the formation of the cosmic microwave background.

💡Cosmic Microwave Background (CMB)

The cosmic microwave background is the thermal radiation left over from the Big Bang. The video explains that this radiation was released during the recombination era when electrons combined with nuclei to form neutral atoms, allowing photons to travel freely. The CMB is a key piece of evidence supporting the Big Bang theory and provides a snapshot of the early universe.

💡Matter-Antimatter Asymmetry

Matter-antimatter asymmetry refers to the imbalance between the amounts of matter and antimatter in the universe. The video mentions that more particles were created than antiparticles, which is crucial for the existence of the universe as we know it. This asymmetry allowed some particles to survive annihilation, forming the building blocks of atoms and ultimately, all matter.

Highlights

The universe is composed of atoms, which in turn are made of electrons, protons, and neutrons, and these are composed of quarks.

The number of atoms in the observable universe is estimated to be more than ten quadrillion vigintillion.

The origin of the particles that make up atoms is believed to be the Big Bang.

The Big Bang is not a theory explaining the beginning of the universe, but rather a model of the early universe.

Our current theories are incomplete, and the standard model of cosmology becomes unreliable close to the beginning of time.

The Planck time, about 10^-43 seconds, is the smallest unit of time that can theoretically exist according to quantum mechanics.

The Planck epoch is the first epoch of the universe, where gravity and other forces are expected to have been unified.

Inflation occurred from about 10^-36 to 10^-33 seconds after the Big Bang, during which the universe expanded faster than the speed of light.

Cosmic inflation is a process that destroys any information about what came before it.

The standard model of cosmology is well understood starting at about 10^-12 seconds after the Big Bang.

The universe consisted of quarks and gluons in a quark-gluon plasma, along with other fundamental particles, before the electroweak symmetry breaking.

The Higgs field gained a non-zero potential at about 10^-11 seconds, leading to the particles of the Standard Model obtaining their rest mass.

The universe was too hot for quarks to combine into hadrons like protons and neutrons until about 10^-5 seconds after the Big Bang.

The matter-antimatter asymmetry is one of the biggest unsolved puzzles in physics, with more particles than antiparticles being created.

The Big Bang nucleosynthesis occurred around 20 minutes after the Big Bang, resulting in a universe composed mainly of hydrogen and helium-4.

Recombination happened around 380,000 years after the Big Bang, when electrons finally bound to nucleons to form stable neutral atoms.

The cosmic microwave background (CMB) is the light released as the first stable neutral atoms were formed, providing a record of the early universe.

The formation of the first atoms in the universe is only the beginning of the story, with the heavier elements essential for life formed later.

Brilliant offers a course called 'The Chemical Reaction' that explores the fundamentals of chemistry from the perspective of chemical reactions.

Transcripts

play00:00

This video is sponsored by Brilliant. Stay tuned to the end for a very special offer

play00:04

for Arvin Ash viewers. You and the world around you are made up of

play00:07

millions and millions of atoms, heck there are estimated to be more than ten quadrillion

play00:13

vigintillion atoms in the observable universe. That is 1 followed by 78 zeroes.

play00:19

But what are atoms? Atoms are tiny particles made from electrons, protons and neutrons,

play00:25

which are in turn composed from quarks. But that raises the question, where did the particles

play00:31

that make up these atoms come from in the first place?

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The short answer is the big bang. In the early universe there was an immense amount of energy,

play00:39

yada, yada, yada - The energy condensed, atoms formed.

play00:43

But as you might suspect, there’s a lot that happened in the yada, yada, yada step.

play00:48

So what really happened? What is the big bang really in a scientific sense? The answer,

play00:53

which might surprise you, is coming up right now…

play01:01

To understand what the big bang really is in a scientific way, we must take a closer

play01:05

look at what happened in the early universe. But to do that, we need to have some kind

play01:10

of a timeline. This means we need some place where this timeline starts.

play01:15

The truth of the matter is that while the big bang is often thought of as the theory

play01:19

explaining the beginning, it’s actually not. We don’t know anything concrete about

play01:26

when the universe actually started, or whether it even did.

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The most we can do is use our best model of the universe, called the standard model of

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cosmology, and use this to turn the clock back to get as close to the beginning of time

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as we can. But if when can do that, why can’t we just turn the clock back to the very beginning,

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at t = 0? In short, the problem is our

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theories are incomplete and at some point, very close to the beginning of time, the theory

play01:55

becomes unreliable. The theory predicts a singularity, a moment in time when all the

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matter and energy in the universe, in other words all of creation was in an infinitesimally

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small point of infinite density. Most physicists believe this is probably wrong.

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The best we can is go back up to one Planck time, about 10^-43 seconds. This is the smallest

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unit of time that can theoretically exist according to quantum mechanics. We have no

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idea what comes before this. So although this is close to the beginning, it not quite t=0.

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Even to understand what happens here at 10^-43 seconds, we would need a quantum theory of

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gravity, because it is here where gravity, the theory of the very large, meets quantum

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mechanics the theory of the very small because all matter and energy, and thus gravity would

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be confined presumably to the tiny scales of quantum mechanics.

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This 10^-43 seconds is considered the first epoch of the universe and is often called

play02:57

the Planck epoch or era. Around this Planck epoch we expect that there

play03:01

was a point at which all the forces; electromagnetism, the weak and the strong force united with

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gravity forming one grand unified force. So, to build a timeline for our big bang theory

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we start before the Planck epoch and set the clock to zero at this point. Keep in mind

play03:18

that this is not really t=0, but we start here anyway because it’s the best we can

play03:22

do without running into the singularity. There might have been something before, but we don’t

play03:28

know, and we also don’t really know how the universe looked during this epoch or what

play03:34

happened. The earliest time we can theorize what happened

play03:37

is around the time of inflation. This happened from about 10^-36 seconds to about 10^-33

play03:45

seconds after the big bang. This is when whatever existed prior to this

play03:50

time, let’s call it the singularity for convenience, grew exponentially fast, faster

play03:55

than the speed of light. This is permissible because there is no theoretical restriction

play04:00

on how fast space can expand. It grew from a point to about the size of a large orange.

play04:08

Now you might say, but I thought you can’t break the speed of light! But actually, you

play04:12

can. What Einstein’s found is that information can’t be transferred faster than the speed

play04:19

of light. This ensures that you always have a cause and then effect. Causality is preserved.

play04:25

But because cosmic inflation occurred faster than the speed of light, it means that two

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points in space that could affect each other before inflation, in other words, two points

play04:35

that were causally connected, might not be causally connected after inflation, since

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they moved apart faster than light. The things we currently understand occur mostly

play04:46

after inflation. Thus, the proper way to understand the term

play04:49

“big bang”, is not as some point or object from which the universe started or came into

play04:54

existence, but as a period in the early universe, when the universe was very hot, very dense,

play05:00

and expanding rapidly. So the big bang is NOT what happened at t=0,

play05:05

it’s everything that happened after that. Inflation is thought to have occurred from

play05:10

10-36 to about 10-33 seconds . Where did the energy come from to cause this rapid expansion?

play05:19

This problem has not been solved. Cosmic inflation is a process that destroys any information

play05:25

about what came before it. The theory of the standard model of cosmology

play05:29

is really only well understood starting at about 10-12 seconds, because the universe

play05:36

at this point had energies that can be approximately replicated in current particle accelerators.

play05:42

Prior to this timeframe, we can only speculate. So, anything that we talk about prior to this

play05:48

is largely speculation. We can turn the clock scientifically almost all the way back, but

play05:53

not quite. We don’t know much about what happened during

play05:56

the period after inflation from about 10-33 seconds to 10-12 seconds.

play06:01

In terms of the forces, gravity is thought to have separated from the unified force shortly

play06:08

after the Planck Epoch at 10^-43 seconds. And later, the strong force is thought to

play06:13

have separated at around the time of inflation 10^-32 seconds. But from 10^-32 seconds to

play06:21

10^-12 seconds, the electromagnetic and weak forces were still united as the electroweak

play06:26

force. And at this point, the laws of the standard

play06:29

model of particles physics tells us the universe probably consisted of quarks and gluons existing

play06:34

together in a quark-gluon plasma, along with some other fundamental particles.

play06:39

But importantly at this point all these fundamental particles were massless, because the Higgs

play06:44

field was massless at this point – in other words, it has not gained a non-zero potential

play06:50

that allows fundamental particles to gain mass by interacting with it.

play06:53

Where these initial massless fundamental particles came from is still not known. It's possible

play07:00

they somehow condensed from the energies present at the big bang, or there might have been

play07:05

an initial scalar field, similar to the Higgs field, called the inflation field, which consisted

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of Inflatons that decayed to the fundamental particles we see today.

play07:15

As time ticks slightly forward to about 10^-11 seconds, and the temperature of this hot universe

play07:21

falls a bit further to about 10^15 or one quadrillion Kelvin. The lower temperatures

play07:27

and energies leads to something called electroweak symmetry breaking and the beginning of the

play07:32

quark epoch. What happens this stage is that the electromagnetic and weak forces become

play07:37

distinct and separate forces. This leads to the Higgs field gaining a non-zero

play07:42

potential – which looks like a Mexican hat called a Sombrero. This means that the fundamental

play07:48

particles that now interact with the Higgs field, gain mass. This is how the particles

play07:53

of the Standard Model obtained their rest mass.

play07:56

If you want to learn more about the electroweak symmetry breaking and how Higgs potential

play08:00

causes the particles to become massive, check out my video about electroweak theory.

play08:05

At this point we have all the building blocks for atoms. Again the time is around 10-11

play08:11

seconds after the beginning, and the temperature of the universe is around 1 quadrillion Kelvin.

play08:16

The universe is however still too hot for the quarks to combine together to form hadrons

play08:22

like protons and neutrons. This changes as the universe keeps expanding

play08:27

and further cooling takes place. As temperatures cool to around 1 trillion Kelvin at 10-5 seconds,

play08:35

the quark plasma turns into a hadron gas consisting of protons, neutrons, and some mesons. The

play08:41

Mesons are a combination quark, anti quark pairs that eventually decay into photons and

play08:46

electrons. As the universe keeps cooling down, the antiparticles

play08:50

now begin annihilating with particles creating lighter particle and antiparticle pairs, eventually

play08:57

ending up as the lightest particles - neutrinos and photons.

play09:01

While we would expect that an equal amount of particle and anti-particles would be created,

play09:06

this didn’t happen. For some reason more particles were created than antiparticles,

play09:12

about one in 10 billion more. The reason for this matter-antimatter asymmetry is one of

play09:18

the biggest unsolved puzzles in physics. If this annihilation were symmetric, meaning

play09:23

the same amount of particles and antiparticles were converted, then we would have had a universe

play09:28

consisting of nothing except photons and neutrinos, that is, no quarks or electrons, and thus

play09:35

no atoms. Luckily there were ever so slightly more particles

play09:38

than anti-particles, so that some quarks and electrons survived the annihilation, and protons,

play09:44

neutrons and electrons that would eventually turn into the first atoms, were able to be

play09:48

formed. This annihilation of particles ends with the

play09:52

lepton epoch at around the 1 second mark. The temperatures at this stage cooled down

play09:58

to around 5 billion Kelvin. Leptons are the lightest matter particles and therefore the

play10:04

last particles to finish this annihilation process.

play10:08

After this fire show, most of the matter particles in the universe had been destroyed and turned

play10:12

into photons and neutrinos. But as I said, because of the mysterious matter-antimatter

play10:17

asymmetry, a few protons, neutrons, and electrons were left over, the building blocks needed

play10:23

for atoms. Protons on their own are technically hydrogen

play10:27

nuclei. You can think of them as positively charged or ionized hydrogen atoms. But we

play10:33

are interested in where the stable neutral atoms come from. To do this, more time had

play10:39

to pass, and physics had do its thing. When the universe was a few minutes old, the

play10:44

temperature dropped below 1 billion Kelvin and it reached the point of the big bang nucleosynthesis,

play10:51

also called the BBN. Initially protons and neutrons were produced

play10:56

in equal numbers, but free neutrons are actually not stable, unlike protons. This is related

play11:02

to the fact that neutrons are slightly heavier than protons, making them less stable than

play11:07

protons. If left free, a neutron will undergo something called beta decay, via the weak

play11:12

force, into a proton in about 10 to 15 minutes. After the protons and neutrons were formed,

play11:18

the temperature was so hot, that the conversion from proton to neutrons, was equal to the

play11:23

conversion from neutron to protons. But as the universe cooled down, this process changed

play11:29

and the decay of neutrons began to dominate. As it turns out, neutrons can become stable

play11:33

when they are in a bound state with other neutrons and/or protons, but not on their

play11:38

own. So, at this point in the story, it was a race

play11:41

against time for these free neutrons to bind with other hadrons and form larger nuclei before

play11:48

they decayed. The big bang nucleosynthesis lasts for around

play11:53

17 minutes until the universe is around 20 minutes old. During this process, a lot of

play11:58

neutrons manage to form bound states and thus survive, but many decayed into protons. And

play12:05

this why we have a lot more protons around today compared to neutrons.

play12:10

The result of this process is that the universe at about 20 minutes, has a nucleon content

play12:15

of around 75% Hydrogen and 25% Helium-4, with very small amount of deuterium, which is an

play12:22

isotope of hydrogen with an additional neutron, a very small amount of Helium-3 and small

play12:27

traces of Lithium-9 nuclei. The universe consisted of about 87% protons and 13% neutrons.

play12:35

So, we see that most of the universe at this point is just protons or Hydrogen nucleons.

play12:41

Pay attention to the fact that at this point in time it’s all ionized nuclei, so only

play12:47

the core of the atoms exists – no electrons bound to them.

play12:51

In order to form neutral atoms, the negatively charged electrons must attach themselves to

play12:58

the positively charged nucleons to balance out the charges.

play13:01

The problem is that the universe is still so hot that the electrons can only attach

play13:05

to the nucleons for a split second before being ripped away because they have so much

play13:10

energy. This also means that at this point the universe

play13:12

is still opaque. If you were there, you wouldn’t see anything, because the photons that carry

play13:17

light would be constantly interact with the nucleons and electrons flying around. They

play13:22

would not be free to propagate through space. The situation with the electrons and the nucleons

play13:27

is analogous to a spacecraft trying to orbit a planet. If the craft flies too fast, then

play13:35

it will fly out of orbit, so it needs to be slow enough for gravity to capture the spacecraft

play13:41

into an orbit around planet. The same thing with the electron – it can’t

play13:44

get bound to the nucleon. Now this photon epoch lasts for a very long time – about

play13:49

380,000 years until the universe cools down to 3000 Kelvin. At this point the electrons

play13:57

have so little energy left that the electromagnetic force can finally bind them to the nucleons

play14:03

for good and form stable neutral atoms. This is called recombination.

play14:09

This also means that the photons are no longer bound in this chaos of positive nucleons and

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negative electrons. They are now free to fly unobstructed through the universe. And we

play14:20

would be able to see this light if we were there in space.

play14:23

The consequence of this today is that everywhere you look, you can see this first light of

play14:28

the universe. This is called the cosmic microwave background or CMB. This light was released

play14:35

as the first stable neutral atoms were formed. So the baby pictures of the universe that

play14:40

you see here is also the record of the first neutral atoms forming in the universe. I made

play14:46

a video about the CMB if you want to learn more.

play14:50

Now the story of how the first atoms in the universe formed, is only the beginning of

play14:55

the fascinating journey of atoms. It is the story of only how the lightest elements formed

play15:00

– Hydrogen, helium and Lithium and some isotopes. But as you know, we need a lot more

play15:05

than that for life to exist. So the next question is, how did the rest

play15:10

of the elements of the periodic table form, particularly where did Carbon, Oxygen, and

play15:15

Nitrogen – elements essential for life, come from?

play15:18

That fascinating story will be the subject of my next video. So, stay tuned for that.

play15:23

In the meantime, if you want to learn about how atoms which form the molecules that take

play15:28

part in the rich landscape of chemical reactions, you will love a course called, “The Chemical

play15:33

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In this course, you’ll learn the fundamentals of chemistry from the perspective of chemical

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It’s different than the usual quantum mechanical approach. And you’ll end up learning and

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Brilliant has a special off for Arvin Ash viewers right now. If you are among the first

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to click the link in the description. And if you have a question, please post it

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in the comments, and I will do my best to answer it. I’ll see you in the next video

play16:24

my friend.

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