Verified Solution • 2025–26 Session moderate

QJEEM21Ch3a96: JEE Main 2021 Chemistry - Class 11 JEEM21Ch3a96 Solution: The number of photons emitted by a monochromatic (single…

The number of photons emitted by a monochromatic (single frequency) infrared range finder of power 1 mW and wavelength of 1000 nm, in 0.1 second is x ×\times 1013. The value of x is _____________. (Nearest integer)

(h = 6.63 ×\times 10 −- 34 Js, c = 3.00 ×\times 108 ms −- 1)

Step-by-Step Verified Solution

Energy emitted in 0.1 sec.

= 0.1 sec. ×\times 10−3Js{10^{ - 3}}{J \over s}

= 10 −- 4 J

If 'n' photons of λ\lambda = 1000 nm are emitted, then 10 −- 4 = n ×\times hcλ{{hc} \over \lambda }

⇒10−4=n×6.63×10−34×3×1081000×10−9\Rightarrow {10^{ - 4}} = {{n \times 6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {1000 \times {{10}^{ - 9}}}}

⇒\Rightarrow n = 5.02 ×\times 1014 = 50.2 ×\times 1013

⇒\Rightarrow 50 (nearest integer)

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