Dual Nature of Matter

JEE Main level, single correct, medium

144 of 200

Question 144 of 200

A metal exposed to light of wavelength 800nm800nm and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500nm500nm is used. The work function of the metal is
(Take hc=1230eV−nmhc=1230eV-nm).

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Answer: (C) 0.615eV0.615eV

According to Einstein's photoelectric equation
kmax=hcλ−ϕ{k}_{max}=\dfrac{hc}{\lambda }-\phi
⇒k1=1230800−ϕ...(1)\Rightarrow {k}_{1}=\dfrac{1230}{800}-\phi ...\left(1\right)
And ⇒k2=1230500−ϕ\Rightarrow {k}_{2}=\dfrac{1230}{500}-\phi
Since, k2=2k1{k}_{2}=2{k}_{1}
⇒2k1=1230500−ϕ...(2)\Rightarrow 2{k}_{1}=\dfrac{1230}{500}-\phi ...\left(2\right)
Eliminating k1{k}_{1} from (1) and (2) we get
0=1230500−1230400+ϕ0=\dfrac{1230}{500}-\dfrac{1230}{400}+\phi
⇒ϕ=0.615eV\Rightarrow \phi =0.615eV

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