Electrons in a sample of gas containing hydrogen-like atom `(Z = 3)` are in fourth excited state. When photons emitted only due to transition from third excited state to second excited state are incident on a metal plate photoelectorns are ejected. The stopping potential for these photoelectorns is `3.95 eV`. now, if only photons emitted due to transition from fourth excited state to third excited state are incident on the same metal plate, the stopping potential for the emitted photoelectrons will be appoximetely equal to

Options

A. `0.85V`
B. `0.75V`
C. `0.65V`
D. `none of these

Answer

B

Explanation

`hv=13.6(3)^(2)[1/4^(2)-1/5^(2)]=2.75eV` for transition from `4^(th)` to `3^(th)` excited state ` hv=(13.6)xx(3)^(2)[1/3^(2)-1/4^(2)]=5.95eV`
For transition from `3^(rd)` to `2 ^(nd)` excited state
`3.95=5.95-phi Rightarrowphi=2eV`
for longer wavelength `eV_(s)=2.75-2=0.75eV`