Electrons in hydrogen like atom `(Z= 3)` make transition from the fifth to the fourth orbit and from the third orbit. The resulting radiation are incident normally on a metal plate and eject photoelectrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is 3.95 volts. Calculate the work function of the metal and the stopping potential for the photoelectron ejected by longer wavelength
(Rydberg constant` = 1.094 xx10^(7) m^(-1)`

Answer

`2`

Explanation

The stopping potential for shorter wavelength is `3.95` volt i.e., maximum kinetic energy of photoelectrons corresponding to shorter wavelength will be `3.95 eV`. Further energy of incident photons corresponding to shorter wavelength will be in transition from `n=4` to `n=3`
`E_(4-3)=E_(4)-E_(3)=(-(13.6)(3)^(2))/((4)^(2))-[(-(13.6)(3)^(2))/((3)^(2))]=5.95 eV`
Now from the equation,
`K_(max)=E-W`
we have, `W=E-K_(max)=E_(4-3)-K_(max)`
`=(5.95-3.95)eV`
`=2eV`