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Question
The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
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Solution
Work function of the metal, `phi_0` = 4.2 eV
Charge on an electron, e = 1.6 × 10−19 C
Planck’s constant, h = 6.626 × 10−34 Js
Wavelength of the incident radiation, λ = 330 nm = 330 × 10−9 m
Speed of light, c = 3 × 108 m/s
The energy of the incident photon is given as:
E = `(hc)/lambda`
= `(6.626 xx 10^(-34) xx 3 xx 10^8)/(330 xx 10^(-9))`
= 6.0 × 10−19 J
`= (6.0 xx 10^(-19))/(1.6 xx 10^(-19))`
= 3.76 eV
It can be observed that the energy of the incident radiation is less than the work function of the metal. Hence, no photoelectric emission will take place.
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