The photons from the Balmer series in Hydrogen spectrum having wavelength between `450 nm` to `700 nm` are incident on a metal surface of work function `2 eV` Find the maximum kinetic energy of ejected electron (Given hc = 1242 eV nm)`

Answer

`0.55 eV`

Explanation

Wavelengths corresponding to minimum wavelength `(lambda_("min"))` or maximum kinetic energy. `(lambda_("min"))` belonging to Balmer series and lying in the given range (450 nm to 750 nm) corresponding to transition from (n=4 to n=2). Here,
`E_(4)= - 13.6/((4)^(2))= -0.85 eV`
`E_(2)=13.6/((2)^(2))= -3.4 eV`
`:. DeltaE=E_(4)-E_(2)=2.55 eV`
`K_("max'")=` Energy of photon - work function
`=2.55-2.0=0.55 eV`