Dual Nature of Matter

JEE Main level, single correct, medium

180 of 200

Question 180 of 200

The maximum velocity of the photoelectrons emitted from the surface is vv when light of frequency nn falls on a metal surface. If the incident frequency is increased to 3n3n, the maximum velocity of the ejected photoelectrons will be:

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Answer: (A) more than 3v\sqrt{3}v

According to Einstein's photoelectric effect,
KEmax⁡=hcλ−ϕK{E}_{\max }=\dfrac{hc}{\lambda }-\phi
The incident energy of the photon is E1=12mv2=hn−ϕ...(1){E}_{1}=\dfrac{1}{2}m{v}^{2}=hn-\phi ...\left(1\right)

If incident frequency increased to 3n

E2=12mv22=3hn−ϕ{E}_{2}=\dfrac{1}{2}m{v}_{2}^{2}=3hn-\phi

=3(hn−ϕ)+2ϕ=3\left(hn-\phi \right)+2\phi

E2=3E1+2ϕ{E}_{2}=3{E}_{1}+2\phi

⇒12mv22=32mv2+2ϕ\Rightarrow \dfrac{1}{2}m{v}_{2}^{2}=\dfrac{3}{2}m{v}^{2}+2\phi

⇒v22=3v2+4ϕm\Rightarrow {v}_{2}^{2}=3{v}^{2}+\dfrac{4\phi }{m}

⇒v2>v3\Rightarrow {v}_{2}\gt v\sqrt{3}

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