Our eye can detect 5 times 10^4 photons per s | vedclass

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Question

(A) The energy of a single photon of green light is given by $E = \frac{hc}{\lambda} = \frac{12400 \ eV \cdot \mathring{A}}{5000 \ \mathring{A}} = 2.4

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$5$

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(A) The energy of a single photon of green light is given by $E = \frac{hc}{\lambda} = \frac{12400 \ eV \cdot \mathring{A}}{5000 \ \mathring{A}} = 2.48 \ eV$. Converting this to Joules: $E \approx 2.48 	imes 1.6 	imes 10^{-19} \ J \approx 4 	imes 10^{-19} \ J$. The minimum intensity the eye can detect is $I_{Eye} = (5 	imes 10^4 \ photons/m^2 \cdot s) 	imes (4 	imes 10^{-19} \ J/photon) = 2 	imes 10^{-14} \ W/m^2$. The ratio of sensitivity is given by the ratio of the intensities: $\frac{S_{Eye}}{S_{Ear}} = \frac{I_{Ear}}{I_{Eye}} = \frac{10^{-13} \ W/m^2}{2 	imes 10^{-14} \ W/m^2} = 5$. Thus,the eye is $5$ times more sensitive than the ear.

Our eye can detect $5 \times 10^4$ photons per second per square meter of green light $(\lambda = 5000 \ \mathring{A})$. If the ear can detect $10^{-13} \ W/m^2$,how many times more sensitive is the eye compared to the ear?

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