Dual Nature of Matter

JEE Main level, numerical answer, medium

168 of 200

Question 168 of 200

A beam of electromagnetic radiation of intensity 6.4×10−5W/cm26.4\times {10}^{-5}\text{W}/{\text{cm}}^{2} is comprised of wavelength, λ=310nm\lambda =310nm . It falls normally on a metal (work function ϕ=2eV\phi =2eV ) of surface area of 1cm21{cm}^{2} . If one in 103{10}^{3} photons ejects an election, total number of electrons ejected in 1s1s is 10x{10}^{x} . (hc=1240eVnm,1eV=1.6×10−19J),\left(hc=1240eVnm,1eV=1.6\times {10}^{-19}J\right), then xx is ___________

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Answer: 11

Energy of photon. E=1240310(nm)=4eV>2eVE=\dfrac{1240}{310\left(\text{nm}\right)}=4eV\gt 2eV (So photoelectric effect will take place)
=4×1.6×10−19=6.4×10−19joule=4\times 1.6\times {10}^{-19}=6.4\times {10}^{-19}joule
Number of photons falling per second

=6.4×10−5×16.4×10−19=1014=\dfrac{6.4\times {10}^{-5}\times 1}{6.4\times {10}^{-19}}={10}^{14}
Number of photoelectron emitted per second

=1014103=1011=\dfrac{{10}^{14}}{{10}^{3}}={10}^{11}

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