Question

In hydrogen atom, during the transition of electron from n^th outer orbit to first Bohr orbit, a photon of wavelength `lambda` is emitted. The value of 'n' is [R =Rydberg's constant] ____________.

Options

• `sqrt ((lambda "R" - 1)/(lambda "R"))`

• `sqrt (lambda "R" (lambda "R" - 1))`

• `sqrt ((lambda "R")/(lambda "R" - 1))`

• `sqrt (lambda ("R" - 1))`

Answer 1

In hydrogen atom, during the transition of electron from n^th outer orbit to first Bohr orbit, a photon of wavelength `lambda` is emitted. The value of 'n' is `sqrt ((lambda "R")/(lambda "R" - 1))`.

Explanation:

`1/lambda = "R" (1/1^2 - 1/"n"^2) = "R" (1 - 1/"n"^2)`

`1/("R"lambda) = 1 - 1/"n"^2 Rightarrow 1/"n"^2 = 1 - 1/("R" lambda) = (lambda "R" - 1)/("R" lambda)`

`therefore "n"^2 = ("R"lambda)/(lambda "R" - 1)    "n" = sqrt("R"lambda)/(lambda"R" - 1)`