Question

A sample of hydrogen gas containing some atoms in one excited state emitted three different type of photons.It is exposed to radiation of 2.88 eV. It emitted 10 different photons while returning to ground state. Which of the following is true?

• A. Principal quantum number of the initial excited state is 3
• B. Principal quantum number of final excited state is 5
• C. The maximum energy of the initially emitted photon is 12.08 eV
• D. The minimum energy of the final emitted photons is 1.88 eV

Answer 1

Answer: (A), (B), (C)

The correct options are
A Principal quantum number of the initial excited state is 3
B Principal quantum number of final excited state is 5
C The maximum energy of the initially emitted photon is 12.08 eV

Number of photons initially$\text{= number of lines = 3 =}\frac{n_1(n_1-1)}{2}$
So, $n_1$ = 3
Number of photons finally $\text{= number of lines = 10 =}\frac{n_2(n_2-1)}{2}$
So, $n_2$ = 5
Maximum energy = $E_3-E_1$
= $\Delta E$ = 13.6 $(1-\frac{1}{3^2})$ = 12.08 eV
Minimum energy = $E_5-E_4$ = $\Delta E$ = 13.6( $\frac{1}{4^2}-\frac{1}{5^2})$ = 0.306 eV