Question

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

Short answer

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

Step-by-step solution

Describe the expression of energy of the photon

The energy Eof 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.

$$\begin{gathered} \mathrm{P}=3.9\times {10}^{26}\mathrm{W} \\ \mathrm{\lambda }=590\mathrm{nm} \\ \mathrm{h}=6.626\times {10}^{-34}\mathrm{J}.\mathrm{s} \\ \mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$

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