Hydrogen atom from excited state comes to the ground by emit... | Physics | SolveeIt | Solveeit

Today, August 19

Question

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$ The value of principal quantum number 'n' of the excited state will be :(R : Rydberg constant)

A

$\sqrt{\frac{\lambda R }{\lambda-1}}$

B

$\sqrt{\frac{\lambda R}{\lambda R-1}}$

C

$\sqrt{\frac{\lambda}{\lambda R -1}}$

D

$\sqrt{\frac{\lambda R ^2}{\lambda R -1}}$

Answer

$\sqrt{\frac{\lambda R}{\lambda R-1}}$

Explanation

Solution

(n)2−Rch+1Rch=λhc
n2−R+R=λ1
R−λ1=n2R
λλR−1=n2R
n2=λR−1λR⇒n=λR−1λR