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JEE Mains · Physics · STD 12 - Dual nature of radiation and matter
- JEE Mains 2020
- Hard
- Numerical
A beam of electromagnetic radiation of intensity \(6.4 \times 10^{-5}\; \mathrm{W} / \mathrm{cm}^{2}\) is comprised of wavelength, \(\lambda=310 \;\mathrm{nm} .\) It falls normally on a metal (work function \(\varphi=2 \;\mathrm{eV}\) ) of surface area of \(1\; \mathrm{cm}^{2} .\) If one in \(10^{3}\) photons ejects an electron, total number of electrons ejected in \(1 \;s\) is \(10^{\mathrm{x}}\).then \(\mathrm{x}\) is \(\left(\mathrm{hc}=1240\; \mathrm{eV} \mathrm{nm}, 1\; \mathrm{eV}=1.6 \times 10^{-19} \;\mathrm{J}\right)\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(11\)
Step-by-step Solution
Detailed explanation
Power incident \(P=I \times A\)
\(\mathrm{n}=\mathrm{no} .\) of photons incident/second
\(\mathrm{nE}_{\mathrm{ph}}=\mathrm{IA}\)
\(\mathrm{n}=\frac{\mathrm{IA}}{\mathrm{E}_{\mathrm{ph}}}\)
\(\mathrm{n}=\frac{\mathrm{IA}}{\left(\frac{\mathrm{hc}}{\lambda}\right)}=\frac{6.4 \times 10^{-5} \times 1}{\frac{1240}{310} \times 1.6 \times 10^{-19}}\)
\(\mathrm{n}=10^{+14}\) per second
since efficiency \(=10^{-3}\)
no. of electrons emitted \(=10^{+11}\) per second.
\(\mathrm{x}=11\)
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