Vocabulary

**Quantum Model**

Bohr developed this model for the hydrogen atom. He proposed that the electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits

**Ground State**

The lowest possible energy state of an atom or molecule

Background

Neils Henrik Bohr was a Danish physicist and he made fundamental contributions to the understanding of the atomic structure and quantum mechanics. He received the Nobel peace Prize in Physics in 1922. Bohr became famous for his world renowned theory of the atomic structure for the hydrogen atom. Included in the theory, Bohr hypothesized that electrons traveled in orbits around the nucleus and that electrons in the outer orbit determined chemical properties of the atom. Bohr also introduced the idea that electrons had the ability to drop from a higher energy orbit to a lower one while emitting photons in the process.

What is the Bohr Model?

Bohr used data from the hydrogen spectrum and devised a model in which the electrons travel in a circular orbit. The line spectrum of hydrogen indicates that only certain energies are allowed for the electrons in the hydrogen atom. Changes in energy levels in hydrogen emits certain wavelengths of lights. Therefore, the energy of the electrons in the electron is quantized.

Energy-level diagram for electron transitions

Orbit transition diagram – accounts for the experimental spectrum; resulting line spectrum

Why is it Important?

The Bohr Model proposed a possible way electrons move around the nucleus. It also introdcued the idea of quantized energy levels. It laid the foundation for further understanding of electrons.

E = -2.178 x 10-18 J (Z^2/n^2)

E = energy, Z = nuclear charge and n = energy level.

This equation can be used to calculate the change in energy of an electron when the electron changes orbits.

Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 3. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

For hydrogen, Z = 1.

When n =1:

E1 = -2.178 x 10^-18 J (12/12)

E1 = -2.178 x 10^-18

When n =3

E3 = -2.178 x 10^-18 J (12/32)

E3 = -2.42 x 10^-19 J

To find the energy difference between energy levels n=1 and n=3:

∆E = E3 - E1 = (-2.42 x 10^-19 J) - (-2.178 x 10^-18) = 1.936 x 10^-18 J

The positive value for ∆ E indicates that the system has gained energy. Therefore, the wavelength of light that must be absorbed to produce this change is found by:l

= (hc)/ ∆ E = (6.626 x 10^-34 J*s)(3.0 x 108 m/s) / 1.936 x 10^-18 J = 1.027 x 10^-7 m

Calculate the energy change and the wavelength of light emitted when the following transition in energy level occurs in a hydrogen atom: n=4 to n=2

When n=4

E4 = -2.178 x 10^-18 J (1/16) = -1.361 x 10^-19 J

When n=2

E2 = -2.178 x 10^-18 J (1/4) = -5.445 x 10^-19 J

E2 - E4 = -4.084 x 10^-19 J

Wavelength = hc /|E|

Wavelength = (6.63 x 10^-34)(3 x 10^8) / 4.084 x 10^-19

Wavelength = 4.870 x 10^-7 m

(answer: ∆ E = -4.084 x 10-19 J; l = 4.868 x 10-7 m)

Calculate the energy change and the wavelength of light emitted when the following transition in energy level occurs in a hydrogen atom: n=1 to n=4

When n=1

E1 = -2.178 x 10^-18 J (1/1) = -2.178 x 10^-18 J

When n=4

E4 = -2.178 x 10^-18 J (1/16) = -1.361 x 10^-19 J

E4 - E1 = -2.314 x 10^-18 J

Wavelength = hc / |E|

Wavelength = (6.63 x 10^-34)(3 x 10^8) / (2.314 x 10^-18)

Wavelength = 8.596 x 10^-8 m

(answer: ∆ E = 2.042 x 10-18 J; l = 9.732 x 10-8 m)

Calculate the energy change required to emit a light of wavelength of

6.000 x 10-7 m

Wavelength = hc / |E|

6.000 x 10^-7 = (6.63 x 10^-34)(3 x 10^8) / E

E = 3.017 x 10^18 J

(answer: ∆ E = 3.312 x 10-19 J)