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Physics Question on Dual nature of matter

A 200 W200\, W sodium street lamp emits yellow light of wavelength 0.6 μm.0.6 \, \mu m. Assuming it to be 25%25 \% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

A

1.5×10201.5 \times 10^{20}

B

6×10186 \times 10^{18}

C

62×102062 \times 10^{20}

D

3×10193 \times 10^{19}

Answer

1.5×10201.5 \times 10^{20}

Explanation

Solution

The number of photons per sec, n=n = amount of power converted to light / energy of photon
Power converted to light P1=200(25/100)=50WP _{1}=200(25 / 100)=50 W
Energy of photon, Ep=hcλ=6.62×10−34×3×1080.6×10−6=33.1×10−20JE _{ p }=\frac{ hc }{\lambda}=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{0.6 \times 10^{-6}}=33.1 \times 10^{-20} J
Thus, n=5033.1×1020=1.5×1020n =\frac{50}{33.1 \times 10^{20}}=1.5 \times 10^{20}