A desk lamp illuminates a desktop with Light of wavelength $λ$ . The amplitude of this electromagnetic wave is $E_{0}$ . Assuming illumination to be normally on the surface, the number of photons striking the desk per second per unit area $N$ is

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$N = \frac{λ ε_{0} {E_{0}}^{2}}{2 h}$

$N = \frac{λ ε_{0} E_{0}^{2}}{h}$

$D a t a I n s u f f i c i e n t$

$N = \frac{2 λ ε_{0} E_{0}^{2}}{h}$

answer is C.

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Detailed Solution

Energy of each photon $= \frac{h c}{λ}$

If N is the number photons per second per unit area, then Intensity $I = N (\frac{h c}{λ})$

As $I = c \times (energy density)$ ,

$\Rightarrow N \frac{h c}{λ} = c \cdot \frac{1}{2} ε_{0} E_{0}^{2}$

$\Rightarrow N = \frac{ε_{0} λ E_{0}^{2}}{2 h}$

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