Question

Let's use the Bohr model equations to explore some properties of the hydrogen atom. We will determine the kinetic, potential, and total energies of the hydrogen atom in the n=2 state, and find the wavelength of the photon emitted in the transition n=2?n=1.

Find the wavelength for the transition n=3 ? n=2 for singly ionized helium, which has one electron and a nuclear charge of 2e. (Note that the value of the Rydberg constant is four times as great as for hydrogen because it is proportional to the square of the product of the nuclear charge and the electron charge.)

Express your answer in nanometers to three significant figures.

Answer 1

Kinetic energy = 13.6 / n²

Potential energy = - 2*13.6 / n²

Total energy = - 13.6 / n²

Now, put n = 2 in the above three equations,

we get, Kinetic energy = 3.4 eV , Potential energy = -6.8 eV, Total energy = - 3.4 eV

Energy of emiited photon = -3.4 - (-13.6) = 10.2 eV

Wavelength = hc/Energy

Wavelength = 6.63e-34*3e8 / 10.2*1.6e-19

Wavelength = 1.218e-7 m or 121.8 nm

Another method to solve for wavelength is to use rydberg's constant

1/wavelength = - 1.097e7 (1/2² - 1/1² ) Here 1.097e7 is rydberg's constant

wavelength = 121.8 nm

For Helium ,

1/wavelength = 4.39e7 (1/9 -1 /4)

wavelength = 1.64e-7 m or 164 nm