Question

Calculate the wave number of photon emitted during the transition from the orbit n=2 to n = 1 in hydrogen atom (R_H = 109677 cm^–1)

• A. 72740 cm^–1
• B. 83560cm^–1
• C. 82258 cm^–1
• D. 92820cm^–1

Answer 1

The Correct Option is C

The formula to calculate the wave number (ν) of a photon emitted or absorbed during a transition in a hydrogen atom is given by:
 ν = R_H x \((\frac {1}{n_f^2}-\frac {1}{n_i^2})\)
Where: 
R_H = Rydberg constant for hydrogen = 109677 cm^-1 
n_f = final energy level or orbit (n = 1 in this case) 
n_i = initial energy level or orbit (n = 2 in this case)
now by substituting we get:
ν = 109677 x  \((\frac {1}{1^2}-\frac {1}{2^2})\) 
ν = 109677 x (1 - \(\frac {1}{4}\)) 
ν = 109677 x \(\frac {3}{4}\) 
ν ≈ 82257.75 cm^-1
which is approximately 82258 cm^-1, which corresponds to option (C).