Dual Nature of Matter

JEE Main level, single correct, medium

192 of 200

Question 192 of 200

The surface of a metal is illuminated with the light of 400 nm400 \mathrm{~nm}. The kinetic energy of the ejected photoelectrons was found to be 1.68eV1.68 \mathrm{eV}. The work function of the metal is (hc=1240eVnm)(\mathrm{hc}=1240 \mathrm{eV} \mathrm{nm})

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Answer: (B) 1.41eV1.41 \mathrm{eV}

12mv2=eVo=1.68eV⇒hv=hcλ=1240evnm400 nm=3.1eV⇒3.1eV=W0+1.6eV∴W0=1.42eV\begin{aligned} & \frac{1}{2} \mathrm{mv}^2=\mathrm{eV}_{\mathrm{o}}=1.68 \mathrm{eV} \Rightarrow \mathrm{hv}=\frac{\mathrm{hc}}{\lambda}=\frac{1240 \mathrm{evnm}}{400 \mathrm{~nm}}=3.1 \mathrm{eV} \Rightarrow 3.1 \mathrm{eV}=\mathrm{W}_0+1.6 \mathrm{eV} \\ & \therefore \quad \mathrm{W}_0=1.42 \mathrm{eV} \end{aligned}

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