4.1 Development of a New Atomic Model

Summary

This lecture discusses the development of a new atomic model, addressing the limitations of Rutherford's model in explaining the behavior of the nucleus and electrons. It introduces the dual nature of light, behaving as both a wave and a particle, and explores the photoelectric effect, where light interacts with metal to emit electrons. Key concepts include Max Planck’s quantum theory, the relationship between energy and frequency, and Einstein’s photon theory. The lecture also introduces Bohr's model of the atom, focusing on electron orbits, energy states, and the hydrogen atom’s line emission spectrum.

Takeaways

• 🔬 Rutherford's atomic model was incomplete as it didn't explain why the nucleus didn't fly apart despite having positive charges.
• ⚛️ The model also couldn't explain why negatively charged electrons didn't fall into the positively charged nucleus.
• 💡 The development of a new atomic model began with experiments involving light, revealing its wave-particle duality.
• 🌈 Light is a form of electromagnetic radiation, and only a small portion of the electromagnetic spectrum is visible to the human eye.
• 🌊 Two key properties of light waves are wavelength (Lambda) and frequency, which are inversely related to maintain the constant speed of light (C = 3 x 10^8 m/s).
• 📡 The photoelectric effect demonstrated that light must reach a certain frequency before electrons are emitted from a metal surface.
• 📏 Max Planck proposed that energy is emitted in discrete packets called quanta, relating energy to frequency with the formula E = hf.
• ✨ Einstein further developed this by describing light as photons, showing that atoms absorb whole photons, not fractions.
• 🔬 The hydrogen atom's emission spectrum showed that excited atoms release specific wavelengths of light when returning to their ground state.
• 🔭 Niels Bohr proposed a model where electrons move in stable orbits, and only certain energy levels are allowed, explaining why hydrogen emitted discrete spectral lines.

Q & A

Why did scientists need to develop a new atomic model?

Scientists needed a new atomic model because Rutherford's model was incomplete. It didn't explain why the positively charged nucleus didn't fly apart due to the repulsion of like charges, nor did it explain why negatively charged electrons didn't fall into the nucleus due to their attraction to the positive charge.

What is the significance of white light in the development of the atomic model?

White light is significant because it led to the understanding that light behaves as both a particle and a wave. This dual nature helped scientists develop new ideas about atomic structure and the behavior of electrons.

What is the electromagnetic spectrum and how does it relate to light?

The electromagnetic spectrum is a range of all possible frequencies of electromagnetic radiation, including radio waves, visible light, X-rays, and gamma rays. The light we see is a small part of this spectrum, and understanding its properties helped scientists understand atomic behavior.

What are the two basic properties of waves mentioned in the script?

The two basic properties of waves mentioned are wavelength (Lambda), which is the distance between two crests or troughs in the wave, and frequency, which is how many crests pass by every second.

How is the speed of light related to wavelength and frequency?

The speed of light (C) is related to wavelength (Lambda) and frequency (F) by the equation C = Lambda * F. This equation shows that wavelength and frequency are inversely related, meaning if one increases, the other must decrease to maintain the constant speed of light.

What is the photoelectric effect and how does it challenge the continuous wave theory of light?

The photoelectric effect is the emission of electrons from a material when light shines upon it. It challenges the continuous wave theory because electrons are only emitted at a certain minimum frequency, and not at lower frequencies regardless of light intensity, suggesting that light must be quantized rather than continuous.

Who proposed the idea that light is emitted in packets called quanta, and how did this relate to the photoelectric effect?

Max Planck proposed the idea that light is emitted in packets called quanta. This concept related to the photoelectric effect by explaining that only certain frequencies (and thus certain quanta of energy) could cause electrons to be emitted from a material.

What is Planck's constant and how does it relate to the energy of quanta?

Planck's constant (H) is a fundamental physical constant that relates the energy (E) of a quantum to its frequency (F) by the equation E = H * F. It is approximately 6.626 x 10^-34 joule seconds and is crucial for understanding the energy carried by photons.

How did Einstein's explanation of the photoelectric effect build upon Planck's idea of quanta?

Einstein explained that light consists of particles called photons and that atoms and molecules can only absorb whole numbers of photons. This meant that there was a minimum energy required to eject an electron, which explained the observed threshold in the photoelectric effect and built upon Planck's quantized concept of energy.

What are energy states in the context of atomic physics?

Energy states are levels of energy that an atom can have, which include both kinetic and potential energy. The ground state is the lowest energy state, and higher states are called excited states.

How did the study of hydrogen's line emission spectrum contribute to atomic theory?

The study of hydrogen's line emission spectrum showed that light was emitted at specific wavelengths when hydrogen atoms returned to their ground state from an excited state. This indicated that atoms have quantized energy levels and that electrons can only occupy certain stable orbits, which was a key part of the development of quantum theory.

Outlines

00:00

🔬 Understanding Rutherford's Model and the Need for a New Atomic Model

The first paragraph discusses the limitations of Rutherford's atomic model. It explains that Rutherford's model couldn't explain why the positively charged nucleus didn't fly apart and why negatively charged electrons didn’t fall into the nucleus due to electrostatic attraction. To address these issues, scientists developed a new model. Experiments with light revealed that light behaves both as a particle and a wave. The light we see is a form of electromagnetic radiation, which includes radio waves, UV rays, X-rays, and gamma rays. The paragraph introduces key concepts such as the electromagnetic spectrum, wavelengths, and frequency, leading to the constant speed of light (C), which ties the wavelength and frequency together.

05:01

💡 Max Planck and the Introduction of Quanta

The second paragraph introduces Max Planck's work on quantizing electromagnetic radiation. It explains how Planck proposed that energy is emitted in discrete packets called 'quanta,' rather than continuously. Planck's equation (E = hf) relates energy to frequency, with Planck's constant (h) as a key factor. The importance of units in Planck's constant is emphasized, as it ties frequency to energy in Joules. This concept of quanta paved the way for understanding how atoms absorb and emit energy in fixed amounts, which is essential in explaining phenomena like the transparency of glass.

10:01

🌟 Einstein and the Photon Theory of Light

This paragraph expands on Planck’s quantum theory with Einstein’s idea of photons. Einstein proposed that light consists of discrete particles called photons, which atoms can absorb or emit in whole numbers, not fractions. This concept explains the photoelectric effect, where light above a certain frequency causes metal to emit electrons. The idea of light as a continuous wave was refuted, showing that specific frequencies and intensities of light are necessary to knock electrons loose. This theory further clarified the threshold behavior observed in the photoelectric effect.

🚀 Exciting Atoms and the Hydrogen Emission Spectrum

The fourth paragraph discusses how scientists explored the hydrogen atom’s behavior when excited by electricity. When hydrogen gas is excited, it emits a pink light, which, when split, reveals four specific colors or wavelengths. These wavelengths represent the light emitted as excited electrons return to their lower energy or ground states. The paragraph introduces the Bohr model, which suggests that electrons move in stable orbits around the nucleus. Electrons move to higher orbits when they absorb photons and return to lower orbits by emitting photons, corresponding to specific energy levels.

🔭 Bohr's Atomic Model and Quantum Energy States

The final paragraph elaborates on Bohr's atomic model and the concept of energy states in atoms. It explains that electrons in an atom can exist in either a ground state (the lowest energy state) or excited states (higher energy levels). Electrons move between these states by absorbing or emitting photons. The Bohr model proposes that electrons orbit the nucleus in fixed, stable paths, much like rungs on a ladder. This model helps explain why hydrogen emits specific wavelengths of light when electrons transition between these energy levels. However, this model works primarily for hydrogen and has limitations for more complex atoms.

Keywords

💡Rutherford's Model

Rutherford's model of the atom proposed that the nucleus is at the center of the atom and contains positive charges, while electrons orbit around it. However, this model was incomplete as it couldn't explain why the positively charged nucleus didn’t fly apart or why electrons didn’t collapse into the nucleus due to their attraction. The video discusses the need for a new atomic model because of these limitations.

💡Electromagnetic Spectrum

The electromagnetic spectrum refers to the range of all types of electromagnetic radiation, including visible light, radio waves, UV rays, and gamma rays. The video explains that light behaves both as a wave and a particle, and we only see a small part of the electromagnetic spectrum. Examples given include the spectrum ranging from radio waves with long wavelengths to gamma rays with very short wavelengths.

💡Wavelength (λ)

Wavelength, represented by the Greek letter lambda (λ), is the distance between two crests or troughs in a wave. It is a fundamental property of waves, including electromagnetic radiation. In the video, wavelength is inversely related to frequency, and when multiplied together, they result in the speed of light, demonstrating the relationship between wave properties.

💡Frequency (f)

Frequency refers to how many wave crests pass a given point in a second. It is measured in hertz (Hz). In the video, frequency is inversely related to wavelength, meaning that as wavelength increases, frequency decreases. This relationship is crucial for understanding the behavior of electromagnetic radiation, such as light.

💡Photoelectric Effect

The photoelectric effect occurs when light of a certain frequency shines on a metal surface, causing it to emit electrons. This effect shows that light behaves as particles (photons) and has energy quantized in specific packets. The video uses the photoelectric effect to demonstrate how light's particle nature was discovered, contradicting the idea that light is purely a wave.

💡Quanta

Quanta are the discrete packets of energy that electromagnetic radiation is emitted or absorbed in. Max Planck introduced this concept to explain the emission of radiation from heated objects. In the video, quanta are used to explain how energy is not emitted continuously but in small, quantized amounts, fundamentally altering the understanding of light and radiation.

💡Planck’s Constant

Planck’s constant (h) is a fundamental value used to relate the energy of a photon to its frequency. In the video, the constant is introduced as 6.626 x 10^-34 J·s, and it plays a key role in explaining the quantization of energy in photons. This constant is critical in the development of quantum theory, linking energy with electromagnetic waves.

💡Photon

A photon is a particle of light that carries energy proportional to its frequency. In the video, Einstein expanded on the concept of quanta by proposing that light consists of photons, explaining the photoelectric effect. Photons are important in understanding how atoms and molecules absorb and emit light in discrete amounts.

💡Bohr Model

The Bohr model of the atom suggests that electrons orbit the nucleus in specific, stable paths or 'rungs,' and can only move between these orbits by absorbing or emitting energy in the form of photons. The video explains how this model accounts for the energy states of electrons and the emission of light in discrete wavelengths, although it is later shown to work only for hydrogen.

💡Ground State and Excited State

The ground state is the lowest energy state of an atom, while an excited state refers to any state higher in energy than the ground state. In the video, these states are used to explain how electrons move between energy levels by absorbing or emitting photons, which corresponds to the emission spectrum of elements like hydrogen.

Highlights

Rutherford's atomic model couldn't explain why the nucleus, composed of positive charges, doesn't fly apart, and why electrons don't fall into the nucleus despite their attraction.

The study of light led to the development of a new atomic model, as light behaves both as a particle and a wave.

Electromagnetic radiation includes various types, such as radio waves, UV rays, X-rays, and gamma rays, with visible light being just a small part of the spectrum.

Wavelength (lambda) is the distance between crests or troughs, and frequency is the number of crests passing per second; they are inversely related, maintaining a constant speed of light (C).

The photoelectric effect occurs when light shines on a metal, emitting electrons only at a certain minimum frequency, with more intensity producing more electrons.

Max Planck proposed that electromagnetic radiation is emitted in packets called quanta, not continuously, and related energy to frequency with the equation E = HF.

Planck's constant, 6.626 x 10^-34, is key in calculating the energy of photons based on frequency.

The quantum theory explains that atoms and molecules can only absorb or lose whole numbers of photons, leading to a minimum energy threshold required to knock electrons out of place.

Einstein further built on quantum theory by explaining that light consists of photon particles, and atoms must absorb entire photons for excitation to occur.

The photoelectric effect revealed that light must have a minimum frequency to eject electrons, debunking the idea that any continuous light wave could build up energy over time.

The hydrogen atom's line emission spectrum showed discrete wavelengths when excited, indicating that energy is released in specific quantities as the atom returns to its ground state.

Bohr's model of the atom introduced the idea of stable orbits where electrons reside, with electrons jumping between orbits by absorbing or emitting photons.

Bohr proposed that electrons can only exist in specific energy levels or orbits, like the rungs of a ladder, and can't occupy in-between states.

Bohr's model successfully explained the hydrogen atom's spectrum but was limited in its application to more complex atoms.

The energy differences between electron orbits correspond to the wavelengths of light emitted or absorbed, providing the basis for the quantum model of the atom.

Transcripts

So today we're discussing chapter 4

section 1 development of a new atomic

model and this comes about because

Rutherford's model which we previously

discussed was incomplete it didn't

explain why the nucleus which we'll

represent by that ball here uh didn't

just fly apart because if you'll

remember the nucleus is made up of a

bunch of positive charges and if you

have like charges that are really close

to each other they should try to fly

apart but they don't they would have sit

there in the middle and it also didn't

explain why the electrons that are in

the area around the nucleus which are

negatively

charged why these electrons which are

points on here don't just fall into the

nucleus due to their attraction to the

positive charge so they had to develop a

new model and after some experiments

with light they came up with some new

ideas so as they looked into the

properties of white light they figured

out that it could be behave as both a

particle and a

wave now what you have to understand is

that the light we see is a form of

what's known as electromagnetic

radiation now so are radio waves UV

rays uh xrays gamma rays there's all

kinds of different electromagnetic

radiation and we actually see a tiny

part of what's known as the

electromagnetic spectrum and I'll give

you an example right here now you can't

see the labels on it but radio waves and

stuff are down here and it goes through

the visual light is about

here and then it goes all the way

through to what are known as gamma rays

on the end and here are some examples of

the size gamma rays have a wavelength

which is the distance between two

troughs represented by the Greek letter

Lambda

about the size of a

nucleus and there's two properties of

waves two basic properties at least

there is the wavelength Lambda which is

the distance between

two crests or troughs in the wave as

well as what's known as the frequency

and that is how many of these crests

pass by every second now if you take

these two numbers Lambda which is the

distance

between crests and the

frequency which is how many pass per

second and you multiply

them what you end up finding is that it

equals a constant C and this C is a very

important number this is the speed of

light which

is which comes out to 3 * 10 8

m/s approximately

now because C always comes out to be

this number it means that Lambda and F

the wavelength and frequency are

inversely related meaning that if one

goes up the other has to go down in

order to maintain this constant over

here so now that we've looked at uh

light as a wave we're going to look at

the basis for light as a particle and

that comes from a effect in nature known

as the photo electric effect and

basically what the photo El electric

effect is is if you shine light onto a

piece of metal like

this then what you'll get is at a

certain minimum

frequency the metal will start

emitting electrons now before this

frequency if it's anything below this

frequency you won't get get any

electrons at all no matter how much

light you're shining on it however once

you get above this

frequency you'll

start getting electrons shooting off and

the more intense the light the more

electrons you'll get however to increase

the speed of the electrons what you need

to do is increase the frequency and

people were confused about this

threshold down here if you will because

if light were a continuous wave then

what it would do is it would bombard the

electrons and get them moving faster and

faster and faster continuously until

eventually they could escape the atom so

a solution to this phenomenon was

initially proposed by a German Scientist

by the name of Max Plank and what plank

said was that hot objects and things

that emit uh electromagnetic waves like

this uh don't emit them continuously but

rather they released as sort of packets

that still have a

wavelength and he called these packets

quanta now plank was able to relate the

energy of these quanta to their

frequency by the equation eal HF where e

is the energy in Jews H is what is known

as Plank's constant now Plank's constant

is 6 * 6. 626 rather time

10 to the

-34 so an absolutely T minuscule

number Jewel seconds and frequency

is seconds to the 1 now it's important

to use the units on Plank's constant

because if you'll notice you need the S

to cancel out with this S1 and then

you're left with the jewels to give give

you the energy and this is how he was

able to relate frequency to energy and

still maintain a particle idea of light

now building off his equation eal

HF he proposed a new idea which is

something called the quantum which is

basically the

minimum energy that a atom or

molecule can absorb

or uh

lose now this interestingly enough is

the reason why glass a pane of glass is

see-through is

because the photons of visual light

which remember have a frequency because

they are electromagnetic

radiation don't have a high enough

frequency though to have the energy

which equals the Quantum of of the glass

basically they don't carry enough energy

to excite an atom so what they end up

doing is they just pass straight

through now Einstein further built upon

this idea by explaining that light is a

wavelike stream of

particles called

photons and he said that atoms and

molecules could only absorb whole

numbers of photons so you can't have

half a photon you have to absorb the

whole packet if you're going to take the

thing you can't divide it in half like

that and so as you can see if you have

to absorb whole numbers of photons what

you end up happening what you end up

doing is limiting the amount of energy

you can take in at one time if you're

not getting a continuous beam of or a

continuous ray of light constantly

bombarding an

electron then what happens is the

electron quickly absorbs and then

re-emits it'll absorb it and then

quickly Reit the

photon but if you were to have a

continuous wave as many people proposed

what this would do is it would

constantly bombard the electron and any

frequency of light would be able to push

it off if you just had enough intensity

and shined it at the electron for long

enough but Einstein

building on Plank's idea of

quanta explained using photons

that you have to absorb whole

numbers therefore there's a minimum

energy required based on this frequency

here to build up enough momentum to

knock an electron out of place and this

in effect explained the previous mystery

behind the photoelectric effect so now

we're going to be studying the hydrogen

atom line emission spectrum which is a

fancy way of saying uh we're

studying the wavelengths of light that

hydrogen emits when it's excited now

we'll get into all the technical

details about what all those terms mean

but first thing you have to know is that

atoms have

something called Energy

States and what these energy states are

is a measure of the

kinetic energy or the temperature

basically how fast an atom is moving as

well as the potential energy of the atom

and the lowest State an atom can be

in is something called the ground state

and for these explanations I'm going to

use the simple bore model of the

atom which we'll discuss

later however you do need to know that

the lowest energy

state of an atom is called the ground

state and then anything that is higher

energy than the ground state is

called the excited

state now how did people found find this

out so what they did was they decided to

excite the atoms basically what they did

was they

passed an electric current through

hydrogen

gas and what they found was that this

hydrogen gas then emitted a pink

light but when they broke up this light

they found out that it was not a

continuous Spectrum rather it was made

of only four colors in the visible

spectrum and these colors correspond to

the different

wavelengths of Light

released by the hydrogen atoms after

being excited by this electric current

going back to their ground

state so now we'll get back over to

these diagrams I have on the left which

are what are known as bore models of

atoms and they're named after a man

named Neil's

bore and

bore proposed that electrons went around

the atom in stable circular or

elliptical orbits like I have drawn

here and he proposed also that the

lowest energy state was when this

electron was close here which is why I

have the ground state with the electron

very close to the nucleus with a larger

distance in the excited

state and basically he proposed that

electrons could move from this ground

state to the higher state by

absorbing a photon of light and what

this would do it is it would impart more

energy energy into the electron and move

it higher up however he also said there

were only a few select stable orbits

corresponding to these various lines

found in the

Spectrum sort of like the rungs on a

ladder so you can

go from the Bottom

Rung up one two or three but you can't

be on rung 1.5

basically you can increase your

gravitational energy by going up at

whole numbers to stable rungs if you

will corresponding to the stable orbits

and the method for moving between these

rungs or orbits was the absorbing and

reemission of

photons given by the energy difference

between the orbits eal HF so you can see

if there's only a few select orbits

you're only going to get a few select

frequencies when you change the energy

which is why they only got four lines

when they measured the spectrum of

excited hydrogen however further

Advanced

applications came to realize that this

model only works for

hydrogen