All electrons ejected from a metal surface by the incident light of wavelength 200 nm can be stopped before travelling 1 m in the direction of uniform electric field of `4NC^(-1)`. The work function of the metal surface is

Options

A. 2 eV
B. 2.2 eV
C. 4 eV
D. 6.2 eV

Answer

B

Explanation

Given, wavelength, `lambda=200 nm`,
electric field, `E=4NC^(-1)` and distance, d = 1 m
Since, electron is stopped in distance d in the direction of electric field E, then the stopping potential is given as,
`" "V_(s)=E*d=4 times 1=4V`
Energy of photon,
`" "E=1250/lambda_(nm)eV`
`rArr " "E=1250/200=6.2eV`
Einstein.s photoelectric equation,
`" "E=W_(0)+KE`
`rArr " "W_(0)=E-eV`
because `KE_(max)=` stopping potential
`rArr " "W_(0)=6.2-4=2.2 eV`
Hence, the work function of metal surface is 2.2 eV.