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Physics · 2024 · 2 marks
Dual Nature of Radiation and MatterParticle Nature of Light: The Photon2 marksApplyvery short answer
CBSE 2024 · Region 3 · Set 1 · Q20
The minimum intensity of white light that our eyes can perceive is about 0.1 nWm^-2. Calculate the number of photons of this light entering our pupil…
The minimum intensity of white light that our eyes can perceive is about $\displaystyle 0.1 \mathrm{nWm}^{-2}$. Calculate the number of photons of this light entering our pupil (area $\displaystyle 0.4 \mathrm{~cm}^{2}$ ) per second. (Take average wavelength of white light $\displaystyle =500 \mathrm{~nm}$ and Planck's constant $\displaystyle =6.6 \times 10^{-34} \mathrm{Js}$ )
Marking-scheme solution
Total Energy gained per second from photon= IA
\[E=N h v
\]
\[I A=N \times \frac{h c}{\lambda}
\]
\[N=\frac{[I A] \lambda}{h c}
\]
\[N=\frac{\left[0.1 \times 10^{-9} \times 0.4 \times 10^{-4}\right] \times 500 \times 10^{-9}}{6.6 \times 10^{-34} \times 3 \times 10^{8}}
\]
\[N=1.01 \times 10^{4}
\]
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