Electronic Energy Levels of Atoms - Part 1

According to classical physics, Newtons first law suggests that if an electron was traveling in a curved path around the nucleus, it would have an acceleration, due to change in direction. Classical physics also suggests that an accelerating charged particle should continuously emit energy in the form of electromagnetic radiation. This means the electron would have a loss in energy. But then a question might arise. If electrons around nucleus are continuously losing energy then they should ultimately crash into the nucleus. Why doesn’t this happen?.

The structure of atom will be destroyed if electrons crash into the nucleus. So what could be the actual structure of atoms? Would it defy classical physics?.To answer this question, in 1913, Bohr introduced the structure of an atom. He presented the idea of fixed energy and path for electrons. He postulated that electrons revolve around the nucleus in fixed paths having fixed energy. He also presented that electrons can only jump between different paths of fixed energy around the nucleus by absorbing or emitting energy in the form of electromagnetic radiation.

So, when an electron jumps from lower energy level, say n=1, to higher energy level, say n=2, it will absorb a specific amount of energy equal to the energy difference of these two orbitals. The energy is absorbed in the form of electromagnetic radiation.

When an electron jumps from higher energy level, say n=2, to lower energy level, say n=1, then it releases energy equal to the energy difference of these two orbitals. Energy is emitted in the form of electromagnetic radiation.

The energy difference of the two energy levels is given by formula shown on top. v is the frequency of electromagnetic radiation, E2 is energy of 2nd shell, and E1 is the energy of 1st shell, and h is the Planck’s constant. We can also write this expression as shown next.

If energy difference is a positive integer then energy is absorbed. If it is a negative integer then energy is released. Therefore, we can say that energy difference between two energy levels is inversely proportional to the wavelength of radiation. So the higher the energy difference, the shorter will be the wavelength of radiation emitted or absorbed.

The Bohr’s atomic model of carbon is given below. It contains 2 electrons in 1st shell and 4 electrons in 2nd shell.

The Bohr model of Fluorine contains 2 electrons in 1st shell and 7 electrons in 2nd shell.

The Bohr models of Aluminum, Phosphorous, oxygen and lithium are given below.

Bohr was only able to explain the loss or gain of energy between shells. When an electron jumps from a higher energy shell to lower energy shell, a spectral line is obtained because electron emits energy in this case.However, in the presence of a magnetic field, something special happens!. More than one spectral lines are seen. Take a look at the spectral lines without magnetic field and with a magnetic field, illustrated here. This indicate that there are also other energy levels within a shell in which electron can be. These are called orbitals, which we will discuss later.

As we can see, in absence of magnetic field, there is only one spectral line. But in the presence of a magnetic field there are 3 spectral lines. This means that an electron might jump from the orbitals of higher energy level to an orbital of lower energy level. Each orbital has different energy than other orbitals. This means different wavelength of radiation is emitted when electron jumps from these different orbitals. This effect is known as the Zeeman effect.Bohr was also unable to explain splitting of spectral lines in the presence of electric field. This is known as the Stark effect. Bohr failed to explain the atomic spectrum of atoms other than hydrogen.When an electron in an atom jumps from a higher energy level to a lower energy level it emits energy. When it jumps from a lower energy level to a higher energy level it absorbs energy. The amount of energy absorbed or emitted depends on the difference in the energy levels.

Electrons absorb or emit fixed amount of energy and in the form of photons. Photons are discrete packets of energy. For example, a photon of red light has specific energy different from a photon of blue light. If the energy difference between energy levels is equal to energy of photon of a red light, then red light will be emitted or absorbed depending on whether the electron jumps from a higher to a lower or a lower to a higher energy level. Quantization of energy means energy is released or absorbed by electrons in an atom in the form of photons. Electrons are fundamental particles. Each electron has specific energy associated to it depending on the energy level in which it is.

If we pass electromagnetic radiations of different wavelengths through a sample containing atoms, some electrons will absorb a specific wavelength of radiation and excite to a higher energy level. If we observe the light passed through the sample on a screen or recorder, there will be some dark gaps in the spectrum of light. Let’s say red light was absorbed by electrons in an atom. Then on the spectrum, wavelength range of red light will appear dark showing that red light is absorbed by electrons. This resulting spectrum obtained as a result of absorption of light by electrons is termed as absorption spectrum.For example, absorption spectrum of hydrogen is shown here. Dark lines indicate absorption of specific wavelength of radiations by the electron in a hydrogen atom.

When an electron absorbs energy and jumps to a higher energy level, it again jumps to a lower energy level by releasing the same amount of energy that was absorbed. Energy of a specific wavelength released as a result is shown as emission spectral line on a spectrum. Resulting spectrum obtained as a result is termed as emission spectrum. These wavelengths of radiations are only those that were released when electrons jump from higher energy levels to lower energy levels.

We know that electrons behave as particles because they have momentum and they possess specific mass of approximately 9×10^-31kg. In 1924 de Broglie said that any particle having linear momentum can possess wave like properties. de Broglie introduced wavelength as the equation shown.

Let’s derive this equation. According to the Planck's equation, E is equal to hv where v, is the frequency and h is the Planck’s constant. As we know, v is equal to c÷λ. Therefore, the above equation can be written as shown first on the left. According to the Einstein equation, E is equal to m×c², which is shown first, to the right. By substituting E, we get the following equation. m×c² equals to (h×c)÷λ.This, when rearranged, produces the de Broglie equation. λ=h÷(m×c).

In the de Broglie equation we can see that wavelength λ is associated with mass of the particle. Mass and wavelength are inversely proportional to each other which shows that greater the mass of the particle, shorter will be its wavelength.German physicist Max Planck presented a theory that explains the absorption and emission of radiation by a black body. A black body is a body that absorbs all the radiations and none of the radiation is emitted when it is at equilibrium with the environment.

Take a look at this illustration. In this case the temperature of the black body is in equilibrium with the environment.

Now, if we heat this black body, the color will change from black to red. Then on further heating it will change to yellow, and then to blue. But why?.

Let us first understand absorption and emission of radiation. Planck presented that when an electron jumps from one energy level, say E1, to another energy level, say E2, it absorbs energy equal to the energy difference of these two energy levels ∆E. That is, E2 – E1 = ∆E.This energy difference is directly proportional to the frequency of radiation absorbed. We can say that the amount of energy absorbed or emitted by an electron is equal to the energy difference of the energy levels between which the transition happened.h is Planck’s constant and v is the frequency of radiation emitted or absorbed.Now, to understand how a black body changes color on heating we should note that a black body absorbs all the radiation when its temperature is in equilibrium with that of the environment. That is why we call it black body because no radiation is emitted in this case.

The environment temperature is 278K. When we heat a black body it absorbs energy from heat and color changes to red. The amount of energy absorbed by a black body in this case is equal to the energy of red wavelength of radiation. After it has absorbed energy it is now not in equilibrium with the environment. So it will emit same amount of radiation that was absorbed. By emitting same amount of radiation it appears red. We can say that temperature is directly proportional to the energy of radiation absorbed.In the same way if we further increase the temperature then energy equal to the yellow and blue wavelength of radiation will be absorbed and same amount of energy will be emitted to attain equilibrium.

This is an illustration of wavelengths emitted by starts. It shows emission of wavelength of radiation by yellow stars and blue stars. Their corresponding temperatures are also shown.