First slide

Quantum Theory of Light

Question

The minimum light intensity that can be perceived by the eye is about 10^-10 W /m².The number of photons of wavelength
5.6 x10^-7 m that must enter the pupil of are 10^-6m²per sec for vision is approximately (use h =6.6x10^-34 Joule -sec)

Moderate

A

3x10²photons
B

3x10³photons
C

3 x10⁴photons
D

3 x 10⁵photons

Solution

Given that $I = 10^{- 10} W / m^{2} = 10^{- 10} J s^{- 1} m^{- 2}$ Let the number of photons required be n. Then
$\frac{nhv}{10^{- 6}} = 10^{- 10} or n = \frac{10^{- 6} \times 10^{- 10}}{hv} or n = \frac{10^{- 16} λ}{hc} = \frac{10^{- 16} \times (5 \cdot 6 \times 10^{- 7})}{(6 \cdot 62 \times 10^{- 34}) (3 \times 10^{8})} = 3 \times 10^{2} photons$

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