JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Modern Physics

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Two sources of light emit X - rays of wavelength 1 nm and visible light of wavelength 500 nm , respectively. Both the sources emit light of the same power 200 W . The ratio of the number density of photons of X- rays to the number density of photons of the visible light of the given wavelengths is:

(A) $\frac{1}{500}$ ✓ Correct
(B)500
(C)250
(D) $\frac{1}{250}$

Answer: (A)

Solution

The power of a source is the number of photons it emits per second times the energy of each photon,

P = n \frac{h c}{λ}

. A shorter wavelength means more energy per photon, so fewer photons are needed to carry the same power. With both sources at equal power,

n_{X} \frac{h c}{λ _{X}} = n_{V} \frac{h c}{λ _{V}}

, so the ratio of photon numbers is

\frac{n _{X}}{n _{V}} = \frac{λ _{X}}{λ _{V}} = \frac{1 nm}{500 nm} = \frac{1}{500}

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option

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JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Modern Physics

Solution

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