Question

Suppose a photon is absorbed by the electron in a hydrogen atom in an n= 2 state. What wavelength should the photon have to enable the electron to transition to the n= 4

state? Once the photon is absorbed, what are the various wavelengths of photons that could be emitted by the atom? (Use Bohr approximation).

Answer 1

From the Bohr model, the total energy of the atom in the nth state (electron in the nth orbit) is

(Equation 1)

Atomic number for hydrogen, Z = 1. Substituting the values of Permittivity Constant , Planck's constant h and the charge of the electron e, and mass of the electron m the above equation simplifies to

  (Equation 2)

If a hydrogen atom in state n=2 has to transistion to state n = 4, it has to absorb energy. The required energy can be calculated from the above equation as

  

This energy must be absorbed from the photon. The enrgy of a photon is given by

Energy (in eV), E = hc/   (Equation 3)

where is wavelenght in micrometers.

Therefore, the wavelenght = hc/E. Substituting the values of plancks constant h and velocity of light c and enegy E = 2.55ev we get

= 7.7953 * 10^ (-26) micrometers

= meters

Once this photon is absorbed, the atom is in the 4th energy state. The electron in the 4th orbit has three different possibilities to jump to an inner orbit.

The wavelength of a photon released when an electron jumps from the mth orbit to the nth orbit is given by

Where R is the Rydberg's constant, R =

For Hydrogen atom Z = 1

(1) When the electron jumps from 4th orbit to 3rd orbit

Substituting the values we get the the wavelength as 1.875 m

(2) When the electron jumps from 4th orbit to 2nd orbit

Substituting the values we get the the wavelength as 0.486 m

(3) When the electron jumps from 4th orbit to 1st orbit

Substituting the values we get the the wavelength as 0.0972 m