Dual Nature of Matter

JEE Main level, single correct, medium

98 of 200

Question 98 of 200

Light is incident on a metallic plate having work function 110×10−20 J110 \times 10^{-20} \mathrm{~J}. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ____\_\_\_\_ rad/s. (h=6.63×10−34 J.s)\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J}. \mathrm{s}\right).

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Answer: (B) 1.04×10161.04 \times 10^{16}

From Einstein's photoelectric equation, hν=W+KEh\nu = W + KE.
With zero kinetic energy, hν=Wh\nu = W.
The frequency is ν=Wh=110×10−206.63×10−34=16.59×1014\nu = \frac{W}{h} = \frac{110 \times 10^{-20}}{6.63 \times 10^{-34}} = 16.59 \times 10^{14} Hz.
The angular frequency is ω=2πν=2π×16.59×1014\omega = 2\pi\nu = 2\pi \times 16.59 \times 10^{14}
=104.25×1014=1.04×1016= 104.25 \times 10^{14} = 1.04 \times 10^{16} rad/s.

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