Question

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⏺ A monoatomic source of light opearating at 200 W emits 4×10^20 photons/sec. find wavelength of the light.

(Given h=6.6×10^-34 j/sec , c=3×10^8 m/sec)

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Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Power (P) = 200W
• Number of photon per second (n) = ${\sf 4×10^{20}}$
• Planck's Constant (h) = ${\sf 6.6×10^{-34}J/s}$
• Speed of light (c) = ${\sf 3×10^8\:m/s}$

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Wavelength of light ${\sf (\lambda)}$

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$\color{darkblue}\underline{\underline{\sf Formula\: Used-}}$

$\color{violet}\blacksquare\underline{\boxed{\sf No.\:of\: photon\:per\:second(n)=\dfrac{Power}{Energy\;of\: photon}}}$

and

$\color{violet}\blacksquare\underline{\boxed{\sf Energy\:of\: photon (E)=\dfrac{hc}{\lambda}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\Large\implies{\sf n=\dfrac{P}{E}}$

$\implies{\sf n=\dfrac{P×\lambda}{hc}}$

$\implies{\sf 4×10^{20}=\dfrac{200×\lambda}{6.6×10^{-34}×3×10^9}}$

$\implies{\sf \lambda=\dfrac{4×10^{20}×6.6×10^{-34}×3×10^8}{400} }$

$\implies{\sf \lambda=\dfrac{79.2×10^{-6}}{400}}$

$\implies{\sf \lambda=0.198×10^{-6}}$

$\color{red}\implies{\sf \lambda = 1.9×10^{-7}m}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Wavelength of light is $\color{red}{\sf 1.9×10^{-7}m}$.

Answer 2

Answer:

1.9×10^-7

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