Question

1. A hydrogen atom (Z=1) is in the third excited state. It makes a transition to a different state, and a photon is either emitted or absorbed. Answer the following conceptual questions:
   1. What is the quantum number of the third excited state?
   2. When an atom emits a photon, is the final quantum number of the atom greater than or less than the initial quantum number?
   3. When an atom absorbs a photon, is the final quantum number of the atom greater than or less than the initial quantum number?
   4. How is the wavelength of a photon related to its energy?
   5. Determine the quantum number of the final state and the energy of the photon when the photon is
      1. Emitted with a shortest possible wavelength
      2. Emitted with the longest possible wavelength
      3. Absorbed with the longest possible wavelength

Answer 1

Sol:

(a) The quantum number of ground state is 1, first excited state is 2, second excited state is 3 and third excited state is 4.

(b) When an atom emits a photon, the final quantum number of the atom will be less than the initial quantum number. Beacause electron jumps from higher energy level to lower energy level.

(c) When an atom absorbs a photon, the final quantum number of the atom will be greater than the initial quantum number. Beacause electron jumps from lower energy level to higher energy level.

(d)

Energy of photon is inversely proportional to wavelength.
Means higher energy photon has smaller wavelength.

(e)

i. The final quantum number will be 1.

ii. The final quantum number will be 2, as its initial quantum number is 3.

iii. The final quantum number will be 4, as its initial quantum number is 3.