Dual Nature of Matter

JEE Main level, single correct, medium

96 of 200

Question 96 of 200

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ____\_\_\_\_.
(Given : h=6.63×10−34 J.s\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J}. \mathrm{s} and c=3×108 m/s\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s})

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Answer: (A) 2×10162 \times 10^{16}

Power of laser: P=6P = 6 mW =6×10−3= 6 \times 10^{-3} J/s
Energy of a single photon at wavelength λ=663\lambda = 663 nm:
E=hν=hcλ=6.63×10−34×3×108663×10−9E = h\nu = \frac{hc}{\lambda} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{663 \times 10^{-9}}
E=6.63×3663×10−34+8+9=19.89663×10−17=3×10−19E = \frac{6.63 \times 3}{663} \times 10^{-34+8+9} = \frac{19.89}{663} \times 10^{-17} = 3 \times 10^{-19} J
Number of photons emitted per second:
N=Total Energy per secondEnergy per photon=6×10−33×10−19=2×1016N = \frac{\text{Total Energy per second}}{\text{Energy per photon}} = \frac{6 \times 10^{-3}}{3 \times 10^{-19}} = 2 \times 10^{16}

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