Question

A sample of hydrogen atoms is in excited state (all the atoms). The photons emitted from this sample are made to pass through a filter through which light having wavelength greater than $800nm$ can only pass. Only one type of photons are found to pass the filter. The sample's excited state initially is [Take $hc=1240eV-nm$, ground state energy of hydrogen atom = $-13.6eV$.]

• A. Fifth excited state
• B. Fourth excited state
• C. Third excited state
• D. Second excited state

Answer 1

The correct option is C Third excited state

$800nm$ is in infrared region. So, the transition is done into state with $n>2$
Energy associated with $800nm$ is $E=\frac{hc}{\lambda }=\frac{1240}{800}=1.55eV$
Therefore, transition energy should be less than $1.55eV$.
Energy levels are $-13.6eV,-3.4eV,-1.51eV,-0.85eV,-0.54eV$ and so on.
For only one type to pass to pass filter, the next should not be in infrared.
Therefore the type of photons passing are emitted from transition from $n=4$ to $n=3$.
Therefore, the sample is initially in third excited state.