Question

An electron makes a transition from orbit n = 4 to the orbit n = 2 of a hydrogen atom. What is the wave number of the emitted radiations? (R = Rydberg's constant)

Options

• 4R/16

• 5R/16

• 3R/16

• 2R/16

Answer 1

3R/16

Explanation:

When the electron jumps from the orbit n_i to orbit n_f, the frequency of the emitted photon is given by

`nu = "Rc"(1/"n"_"i"^2 - 1/"n"_"f"^2)`

For transition between n_i = 4 and n_f = 2,

`nu = "Rc" (1/2^2 - 1/4^2) = (3"Rc")/16`

Therefore, wave number of the emitted radiation,

`barnu = 1/lambda = nu/"c" = (3"Rc"//16)/"c" = (3"R")/16`