Question-26 Which of the following transitions in hydrogen atom emit photons of highest frequency? (n = principal quantum number)
(A) n=1\ to\ n=3
(B) n=2\ to\ n=4
(C) n=5\ to\ n=3
(D) n=2\ to\ n=1
Answer : (D)
Explanation:
For Emission of photon in hydrogen atom,
hν = R\left(\frac{1}{n_i^2} - \frac{1}{n_f^2}\right)
⇒ ν ∝ \left(\frac{1}{n_i^2} - \frac{1}{n_f^2}\right)
For n = 1 to n = 3 and n = 2 to n = 4 transitions absorption of photons takes place.
These transitions will not emit photons.
∴ For n = 5 to n = 3 transition,
ν₁ ∝ \left(\frac{1}{3^2} - \frac{1}{5^2}\right) ⇒ ν₁ ∝ \frac{16}{225}
For n = 2 to n = 1 transition,
ν₂ ∝ \left(\frac{1}{1^2} - \frac{1}{2^2}\right) ⇒ ν₂ ∝ \frac{3}{4}
∴ ν₂ > ν₁