Monochromatic light of wavelength 3000 , math | vedclass

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Question

(B) The rate of photon emission (or incidence) is given by the formula $\frac{n}{t} = \frac{P}{E} = \frac{I \cdot A}{hc/\lambda} = \frac{I \cdot A \cd

Vedclass · Accepted Answer

$9 	imes 10^{13} \, s^{-1}$

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(B) The rate of photon emission (or incidence) is given by the formula $\frac{n}{t} = \frac{P}{E} = \frac{I \cdot A}{hc/\lambda} = \frac{I \cdot A \cdot \lambda}{hc}$.Given:Intensity $I = 150 \, mW/m^2 = 150 	imes 10^{-3} \, W/m^2 = 0.15 \, W/m^2$.Area $A = 4 \, cm^2 = 4 	imes 10^{-4} \, m^2$.Wavelength $\lambda = 3000 \, \mathring{A} = 3000 	imes 10^{-10} \, m = 3 	imes 10^{-7} \, m$.Planck's constant $h = 6.63 	imes 10^{-34} \, J \cdot s$.Speed of light $c = 3 	imes 10^8 \, m/s$.Substituting the values:$\frac{n}{t} = \frac{0.15 	imes 4 	imes 10^{-4} 	imes 3 	imes 10^{-7}}{6.63 	imes 10^{-34} 	imes 3 	imes 10^8}$.$\frac{n}{t} = \frac{1.8 	imes 10^{-10}}{19.89 	imes 10^{-26}} \approx 0.0905 	imes 10^{16} = 9.05 	imes 10^{13} \, s^{-1}$.Rounding to the nearest option, the rate is $9 	imes 10^{13} \, s^{-1}$.

Monochromatic light of wavelength $3000 \, \mathring{A}$ is incident on a surface of area $4 \, cm^2$. If the intensity of light is $150 \, mW/m^2$, then the rate at which photons strike the target is:

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