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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# At what rate does the Sun emit photons? For simplicity, assume that the Sun’s entire emission at the rate of ${\mathbf{3}}{\mathbf{.}}{\mathbf{9}}{\mathbf{×}}{{\mathbf{10}}}^{{\mathbf{26}}}{\mathbf{}}{\mathbf{W}}$ is at the single wavelength of 550 nm.

The rate of emitted protons from the Sun is $1.00×{10}^{45}\mathrm{photons}/\mathrm{s}.$

See the step by step solution

## Describe the expression of energy of the photon

The energy E of a photon of wavelength ${\lambda }$ is given by,

${E}{=}\frac{hc}{\lambda }$

Here, h is Planck’s constant, and c is the speed of light.

## Determine the rate of emission of the photon

Assume that the protons are emitted by a rate R from the sodium lamp. Then, the power P of the sodium lamp is equal to the product of rate R and the energy of each photon E.

$\begin{array}{c}P=RE\\ P=R\left(\frac{hc}{\lambda }\right)\\ R=\frac{p\lambda }{hc}\end{array}$ ......(1) Substitute the below values in eq 1.

$\mathrm{P}=3.9×{10}^{26}\mathrm{W}\phantom{\rule{0ex}{0ex}}\mathrm{\lambda }=590\mathrm{nm}\phantom{\rule{0ex}{0ex}}\mathrm{h}=6.626×{10}^{-34}\mathrm{J}.\mathrm{s}\phantom{\rule{0ex}{0ex}}\mathrm{c}=3×{10}^{8}\mathrm{m}/\mathrm{s}\phantom{\rule{0ex}{0ex}}$

Therefore, the rate of emitted protons from the Sun is $1.00×{10}^{45}\mathrm{photons}/\mathrm{s}.$