The work function for the following metals is given Na: 2.75 eV, K:2.30 eV , Mo: 4.17 eV , Ni: 515 eV.
Which of these metals will not give photoelectric emission for a radiation of wavelength 3300 A from a `He-Cd` laser placed 1m away from the photocell? What happens if the laser is brought nearer and placed 50 cm away?

Explanation

Given , wavelength of incident radiation
`lamda =3,300 Å`
Frequency, `v=c/lamda=(3xx10^(8))/(3,300xx10^(-10))`
`=9.02xx10^(14)Hz`
Given , work function for Na,
`(W_0)_(na) = 2.75 eV = 2.75 xx1.6 xx10^(-19)J`
Threshold frequency for Na,
`(v_0)_(Na)=((W_0)_(Na))/h`
`implies(v_0)_(Na)=(2.75xx1.6xx10^(-19))/(6.63xx10^(-34))`
Similarly , for K
`(W_0)_K=2.30eV=2.30xx1.6xx10^(-19)J`
`(v_0)_K=(2.30xx1.6xx10^(-19))/(6.63xx10^(-34))`
`=5.55xx10^(14)Hz`
For Mo,
`(W_0)_(Mo)=4.17eV=4.17xx1.6xx10^(-19)J`
`(v_0)_(Mo)=(4.17xx1.6xx10^(-19))/(6.63xx10^(-34))=1.0xx10^(15)Hz`
For Ni,
`(W_0)_(Ni)=5.15eV=5.15xx1.6xx10^(-19)J`
`(v_0)_(Ni)=(5.15xx1.6xx10^(-19))/(6.63xx10^(-34))=1.24xx10^(15)Hz`
The frequency of incident radiation v is greater than `(v)_(Na) and (v_0)_K` but less than `(V_(0))_(Mo) and (V_0)_(Ni)` Therefore, there will not be any photoelectric emission for Mo and Ni . If the laser is brought closer , intensity of radiation increases, but this does not affect the results regarding Mo and N.. however , photoelectric current from Na and K will increase in proportion to intensity of incident radiation.