The Bohr Model of the atom and Atomic Emission Spectra: Atomic Structure tutorial | Crash Chemistry

Summary

In the late 19th century, scientists observed that energized elements emitted specific colors of light, unique to each element. Niels Bohr, in 1913, used these spectral colors to develop an atomic model explaining electron behavior and energy quantization. His model suggested electrons orbit the nucleus at discrete energy levels, emitting light only when transitioning between these levels. This concept of quantized electrons, supported by Planck's and Einstein's work on light quanta, laid the groundwork for modern quantum mechanics and earned Bohr a Nobel Prize.

Takeaways

• 🌈 The emission spectrum of elements is unique and can be seen when elements are energized.
• 💡 Hydrogen gas emits a specific color spectrum when energized, which our eyes perceive as a single color.
• 🔬 In 1913, Niels Bohr used the emission spectrum to develop a model of the atom explaining electron behavior and emitted colors.
• 🌀 Bohr's model suggested electrons orbit the nucleus at different energy levels, with higher energy corresponding to larger orbits.
• 🚫 Accelerating electrons, as in orbiting, should lose energy and spiral into the nucleus, contradicting Bohr's model.
• 💡 Bohr proposed that electrons only emit light when transitioning between specific energy levels, not during orbiting.
• 🔑 The term 'quantized electron' refers to electrons existing only at discrete energy levels, a key concept in quantum mechanics.
• 📊 Bohr used integers to represent electron orbits, based on Rydberg's mathematical analysis of alkali metal spectra.
• 🔴 The energy of emitted light corresponds to the difference in electron energy between two discrete levels.
• 🏆 Both Max Planck and Albert Einstein contributed to the concept of quantization with their work on light energy and the photoelectric effect.
• 📐 Bohr's model mathematically calculates the energy of emitted light using Planck's constant and the speed of light.

Q & A

What was the remarkable observation made by scientists in the 19th century regarding elements and light?

Scientists observed that energized elements emitted specific visible colors of light, which were unique to each element, but the reason behind this phenomenon was unknown at the time.

How does the human brain perceive the color emitted by energized hydrogen gas?

The human brain integrates the four individual colors emitted by energized hydrogen atoms into one specific color, which appears as a pale pinkish hue.

What is the emission spectrum of hydrogen, and how does it relate to the colors emitted by hydrogen atoms?

The emission spectrum of hydrogen consists of specific wavelengths corresponding to violet, blue, turquoise, and red colors. These are the actual colors emitted by hydrogen atoms when the light is refracted.

How did Niels Bohr use the emission spectrum to create a model of the atom?

Bohr used the emission spectrum to develop a model where electrons orbit the nucleus at specific, discrete energy levels, and emit light only when transitioning between these levels.

What was the major obstacle that Bohr's model presented to early 20th-century physics?

The major obstacle was the contradiction between the observed stable orbits of electrons and the classical physics prediction that accelerating charges (like orbiting electrons) would emit energy and spiral into the nucleus.

What is the significance of the term 'quantized electron' in Bohr's model?

The term 'quantized electron' refers to Bohr's concept that electrons can only exist at specific, discrete energy levels and cannot exist at energies in between those levels.

How did Johannes Rydberg's work contribute to Bohr's model of the atom?

Rydberg's mathematical analysis of alkali metals' emission spectra provided the basis for using integers to represent electron energy levels in Bohr's model.

What is the relationship between the energy levels of an electron and the color of light emitted during transitions?

The energy levels of an electron determine the color of light emitted during transitions. For example, a transition from n=3 to n=2 emits red light, while a transition from n=6 to n=2 emits violet light.

What was Max Planck's contribution to the concept of quantized energy?

Max Planck introduced the idea that light energy, or electromagnetic waves, can only exist at discrete energies, which was a significant step towards the development of quantum theory.

How did Albert Einstein's work on the photoelectric effect support the concept of quantized light?

Einstein's work showed that light, which has no mass, behaves as if it has momentum, suggesting that it can be thought of as particles, or photons, with quantized energy.

What mathematical equation is used to calculate the energy of an emitted photon in Bohr's model?

The energy of an emitted photon can be calculated using the equation E = (hc) / λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.

Why are the electron energies in Bohr's model negative, and what does this signify?

Electron energies are negative to signify that they are bound within the atom by the attractive force of the nucleus. Zero energy is defined as the point where the electron is at an infinite distance from the nucleus.

What type of light would be emitted from an n=5 to n=4 transition in hydrogen?

An n=5 to n=4 transition in hydrogen would emit light in the ultraviolet spectrum, which is higher in energy than visible light.

Outlines

00:00

🌈 The Discovery of Emission Spectra

The paragraph discusses the phenomenon of energized elements emitting specific colors of light, unique to each element, a mystery in the late 19th century. It explains how energizing hydrogen gas results in a specific color spectrum that our eyes perceive as a single color due to the integration of four individual colors. The discovery of the emission spectrum of hydrogen and the development of Niels Bohr's atomic model in 1913, which used these spectral colors to explain electron behavior, is highlighted. Bohr's model suggested electrons orbit the nucleus at discrete energy levels, and that the emitted light's energy equals the energy change of the electron during transitions between these levels. The concept of quantized electrons, which can only exist at specific energies, is introduced as a key contribution to the atomic structure theory.

05:07

🔬 Quantum Theory and the Bohr Model

This section delves into the mathematical foundations of the Bohr model, emphasizing the quantization of light energy proposed by Max Planck and the photoelectric effect explained by Albert Einstein. It describes how these concepts led Bohr to propose that electrons, particles with mass, could also exhibit quantized behavior. The mathematical relationship between the energy of emitted light and the electron's transition between energy levels is explored, using the example of the red light emitted by hydrogen. The paragraph also discusses the significance of the negative electron energy values and the decreasing intervals between energy levels as 'n' increases, which are still relevant in the current quantum mechanical model of the atom.

10:18

🚀 Exploring Higher Energy Transitions

The final paragraph ponders the existence of transitions to lower energy levels, such as n=1, which result in the emission of ultraviolet light. It invites consideration of the type of light that might be emitted during a transition from n=5 to n=4, prompting reflection on the nature of light emission based on energy level transitions. This section serves as a thought experiment to understand the broader implications of the Bohr model and the concept of quantized electron energy levels.

Keywords

💡Emission Spectrum

The emission spectrum refers to the range of wavelengths or colors of light emitted by an energized element. In the video, it is mentioned that energized hydrogen gas emits a specific color spectrum, which is split into four colors when refracted. This phenomenon is key to understanding atomic structure and the behavior of electrons within an atom.

💡Hydrogen Atom

A hydrogen atom is the simplest atomic structure, consisting of one proton and one electron. The video explains how energized hydrogen atoms emit specific colors of light, which are integral to the study of atomic spectra and the development of the Bohr model.

💡Niels Bohr

Niels Bohr was a physicist who proposed a model of the atom in 1913. His model is discussed in the video as a significant contribution to understanding the behavior of electrons and the emission of light by atoms. Bohr's model introduced the concept of quantized energy levels for electrons.

💡Quantized Electron

A quantized electron is an electron that can only exist at specific, discrete energy levels. This concept is central to the video's discussion of Bohr's model, where electrons can only occupy certain orbits with specific energies, leading to the emission of light at specific wavelengths.

💡Energy Transition

An energy transition is the process by which an electron moves from one energy level to another, either absorbing or emitting energy in the form of light. The video describes how transitions between energy levels in a hydrogen atom result in the emission of specific colors of light.

💡Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it is exposed to light of a certain frequency. Albert Einstein's explanation of this effect, as mentioned in the video, contributed to the concept of light quanta, or photons, and earned him a Nobel Prize.

💡Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics, denoted by 'h'. The video explains how this constant, along with the speed of light 'c', is used to calculate the energy of a photon, which is integral to understanding the emission spectrum of hydrogen.

💡Rydberg Formula

The Rydberg formula is used to calculate the wavelengths of the hydrogen spectral lines. The video mentions how Johannes Rydberg's mathematical analysis of alkali metals' emission spectra led to the use of integers to represent electron energy levels in Bohr's model.

💡Electron Orbit

An electron orbit refers to the path that an electron follows around the nucleus of an atom. Although the video clarifies that electrons do not orbit the nucleus in the classical sense, the concept is used to explain the quantized energy levels and the emission of light by electrons transitioning between these levels.

💡Heisenberg's Uncertainty Principle

Heisenberg's Uncertainty Principle states that the position and momentum of a particle cannot both be precisely measured at the same time. The video notes that this principle, introduced by Werner Heisenberg, contradicted the idea of electrons orbiting the nucleus in a definite path, a concept from Bohr's model.

💡Quantum Mechanics

Quantum mechanics is the branch of physics that deals with the behavior of particles at the atomic and subatomic level. The video discusses how Bohr's model and the concept of quantized electrons laid the groundwork for the development of quantum mechanics.

Highlights

Energized elements emit specific visible colors of light, unique to the element.

Hydrogen gas emits a specific color spectrum when energized.

The human brain integrates multiple colors into one when viewing an emission spectrum.

Niels Bohr used spectral colors to create an atomic model explaining electron behavior.

Bohr's model suggested electrons orbit the nucleus at different energy levels.

Bohr's model presented a challenge to early 20th-century physics regarding electron stability.

Bohr proposed that electrons only emit light when transitioning between energy levels.

Electrons can only exist at specific, discrete energies, a concept termed quantization.

Bohr's model used integer numbers to represent electron energy levels.

Electron transitions from higher to lower energy levels produce specific colors of light.

The concept of quantized electrons is still valid in the current quantum mechanical model.

Max Planck introduced the idea of quantized light energy, leading to the Nobel Prize.

Albert Einstein's photoelectric effect showed light has momentum, supporting the particle theory of light.

Bohr's model suggested that particles with mass, like electrons, could behave as if quantized.

The mathematical relationship between energy transitions and emitted light was established.

Bohr's model calculated the energy of emitted light using Planck's constant and the speed of light.

Electron energy levels in hydrogen can be calculated using Rydberg's formula.

The energy difference between electron levels corresponds to the energy of emitted light.

Bohr's analysis of light emission is a crucial part of the current quantum mechanical model of the atom.

Electron energies are negative because they are defined as zero at an infinite distance from the nucleus.

Transitions to lower energy levels, such as n=1, emit ultraviolet light, not visible to the human eye.

Transcripts

Welcome to:

In the latter half of the 19th century something remarkable was being noticed by a few scientists.

Energized elements would emit specific visible colors of light, and the colors were specific to the element, but no one knew why this was happening.

For example, if we energize hydrogen gas with an electric current, the H2 molecule is split into hydrogen atoms.

Those energized hydrogen atoms emit a specific color spectrum of four colors.

Our nervous system however is not able to see the four individual colors, our brain integrates those four colors into one specific color, so that’s the color we see.

But when we refract, or split, hydrogen’s pale pinkish color, we can then see the colors that are actually being emitted by hydrogen atoms: violet, blue, a sort of turquoise, and red all at specific wavelengths.

This is the emission spectrum of hydrogen

In 1913, using the atom’s vast empty space provided by Rutherford’s nuclear model of the atom,

Niels Bohr used these spectral colors to create a model of the atom that explained the existence of the emitted colors and explained the behavior of electrons in the atom.

In Bohr’s atomic model the electrons orbit the nucleus.

The electrons have different energies,

and the higher their energy the larger the radius of their orbit.

This model however presented a very large obstacle for early 20th century physics.

It was known that an accelerating charge, which is what these orbiting electrons are,

will emit energy in the form of light,

and so that constant loss of energy would mean the electron would not be able to maintain an orbit,

it would spiral down into the nucleus due to the strong attractive force of the nucleus.

But Bohr said no, that would not happen.

In his model, energy could be absorbed by an electron,

putting it in a higher energy orbit,

and the electron would only then emit light energy,

when the energized electron transitioned from a higher to lower energy.

The energy of the emitted light is equal to the energy change of the electron.

The emission spectrum of any one element is constant, and so Bohr concluded the electrons can only exist at specific, discrete energies in order to produce such specific, discrete emission spectra.

The electrons could not exist at energies in between those discrete energies and this is what is meant by the term quantized electron.

Let’s take a closer look at this last idea, which was a contribution to atomic structure that still holds true in our current quantum mechanical model of the atom.

Bohr numbered his orbits with integers, symbolizing each orbit with the letter n, representing the electron’s energy.

The letter n and the numbering came out of earlier mathematical analyses of alkali metals’ emission spectra

by Johannes Rydberg in 1888,

and so using integers is not arbitrary. They have mathematical significance, which we will see a bit later on.

If we focus on a section of the orbits, we get a diagram of the allowed electron energies in hydrogen. Bohr found that these energies give us hydrogen’s emission spectrum.

An electron transitioning from n = 3 to n = 2 emits a red photon, from 4 to 2 gives a blueish-green color, 5 to 2 gives blue, and 6 to 2 gives violet.

Notice that in the transition, the electron does not exist in between those two allowed energies.

If the electron could exist at any energy, then the changes in electron energy, here represented by delta E, would result in emitting a large spectrum of colors, a continuous rainbow.

But only discrete colors are seen, and so the electron must remain at discrete energies.

Again, this is called a quantized electron, an electron that can only exist at discrete energies. Bohr was very bold to tell the world that the electron was quantized, but there was the work of two other bold scientists to support him.

In 1900, in order to solve a problem in the analysis of ultraviolet light, Max Planck came up with the idea of quantized light energy.

Being that light, in other words electromagnetic waves, cannot have just any energy, they can only exist at discrete energies, which incidentally got him a Nobel Prize.

Five years later in 1905, Einstein took that a giant step further with his photoelectric effect,

experimentally showing that light has momentum,

and momentum is a property derived from mass,

but light has no mass,

so the quantized light wave was behaving as if it was a particle,

which we call a photon,

which, incidentally, got Einstein a Nobel Prize.

SO, with the existence of quantized light behaving like a particle with mass,

in 1913 Bohr looked at the other side of that coin

and found that a particle with mass, such as the electron,

could behave as if it was quantized.

Yes, you guessed it, this got him a Nobel Prize.

Let’s take a more mathematical look at the emission of red light from hydrogen.

Let’s mark the energy transition of an electron with an arrow and delta E.

The energy of any electromagnetic wave can be calculated with hc divided by lambda, which is a combination of these two equations, by substituting c over lambda for nu.

Given that we have the wavelength of the emitted red light, and h and c are constants, we can determine the energy of that red photon. Planck’s constant, h, times the speed of light, c, divided by the wavelength expressed in meters to keep units constant, gives a photon energy of 3.03 x 10^-19 Joules.

In Bohr’s model, that would also be the energy difference of the electron transitioning from n=3 energy to n = 2 energy.

The energy of an electron in hydrogen at any given n can be calculated using this equation derived from Rydberg’s analysis of atomic emission spectra.

Let’s plug in the two integers from n to find the electron’s energy at n = 2 and n = 3. We may see something interesting.

For an electron at n = 3, its energy is -2.42 x 10 ^ -19 joules. For an electron at n = 2, its energy is -5.45 x 10^-19 joules.

The difference between these two energies is the energy lost by the electron as it transitions from n = 3 to n = 2, which would be the energy of the emitted light.

We can see mathematically that the energy lost by an energized electron when transitioning to a lower allowed energy level is emitted as light.

So by determining the energies of emitted light, Bohr was able to work backwards and arrange the allowed energies of electrons by the magnitude of the transitions occurring to produce the observed emission spectrum.

Note that the intervals between each succeeding n decreases as electron energy gets higher.

This came out of Bohr’s analysis of light emission and is still an important part of our current quantum mechanical model of the atom, which begs the question, what else is there about the Bohr model that is still relevant to current understanding of the atom?

Well, we know that electrons DO NOT orbit the nucleus, and that came out of Heisenberg’s Uncertainty Principle 14 years later in 1927, which incidentally was part of Heisenberg’s Nobel Prize.

However, an electron’s most probable distance from the nucleus does increase as the energy of the electron increases, AND, perhaps Bohr’s most important contribution to the eventual quantum mechanical model of 13 years later, is that the electron is quantized, it can only exist at specific energies.

So there are a couple of items that you may have been wondering about:

Why are the electron energies negative? Well, mathematically, an electron’s energy is defined as zero when it is an infinite distance from the nucleus. So an energy sufficiently less than zero is low enough to be held by the attractive force of the nucleus.

You may notice that these energies are very tiny, which is reasonable since it is only the energy of a single electron. You may have also noticed that the energy of the light is likewise very tiny, but that is also reasonable given that it is the energy of a single photon.

A second question: what about n = 1 or other transitions? Bohr did know that hydrogen also emitted ultraviolet light, which is higher energy than visible light. So transitions to n = 1 occur, but they are not visible, they are ultraviolet. What type of light do you think would be emitted from an n = 5 to n = 4 transition? Think about it.