Answer to Question #118774 in Atomic and Nuclear Physics for Jess

Question

What is the wavelength of the photon emitted by a hydrogen atom when a bound electron in the n = 3 state makes the transition to the n = 2 state? (to 2 s.f in nm)

Answer 1

The wavelength of emitted photon by a hydrogen atom when a bound electron in the n = 3 state makes the transition to the n = 2 state is

$\frac{1}{ \lambda }=R[ \frac{1}{n_1^2}- \frac{1}{n_2^2}]$

$=(1.097*10^7 /m)[ \frac{1}{2^2}- \frac{1}{3^2}]$

$=(1.097*10^7 /m)[ 0.13889]$

$\lambda=6.56*10^{-7} m=656 nm$

Hence, the wavelength of emitted photon is $\lambda =660 nm$