Question

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is ______.

Options

• `sqrt((lambda"R")/(lambda"R"-1))`

• `sqrt(lambda/(lambda"R"-1))`

• `sqrt((lambda"R"^2)/(lambda"R"-1))`

• `sqrt((lambda"R")/(lambda-1))`

Answer 1

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is `underlinebb(sqrt((lambda"R")/(lambda"R"-1)))`.

Explanation:

`1/lambda="Rz"^2(1/"n"_1^2-1/"n"_2^2)`

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

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

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

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

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

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