91影视

The power of the sodium light is,P= 10 W

The wavelength of the sodium light is, $\mathrm{位}=589\mathrm{nm}$

The diameter of the eye is, d = 4mm

The distance from the source to the eye is, D = 10m

The time taken in passing the photons is, t = 1s

The expression for the energy of the photons emitted by the light.

E = nhf

Here, E is the energy, n is the number of photons, h is the Planck's constant and f is the frequency

Write the expression for the power of the light as it is equal to the energy of the photons emitted by the light in the given period of time.

Pt = nhf

Here, n is the number of photons, h is the Planck's constant and f is the frequency.

Substitute $\frac{c}{位}$for f in the above expression.

$Pt=nh\frac{c}{位}$

Here, c is the speed of light with the value $2.99脳{10}^{8}m路s^{-1}$, and h is the Planck鈥檚 constant with the value $6.626脳{10}^{-34}\mathrm{J}.\mathrm{s}$.

Substitute all the values in the above expression.

role="math" localid="1660022805511" $$\begin{gathered} 10\mathrm{W}脳\frac{1\mathrm{J}/\mathrm{s}}{1\mathrm{W}}脳1\mathrm{s}=\mathrm{n}脳6.626脳{10}^{-34}\mathrm{J}.\mathrm{s}脳\frac{2.99脳{10}^8}{589\mathrm{nm}脳{\displaystyle \frac{1脳{10}^{-9}\mathrm{m}}{1\mathrm{nm}}}} \\ 10\mathrm{J}=\mathrm{n}脳6.626脳{10}^{-34}\mathrm{J}路\mathrm{s}脳\frac{2.99脳{10}^8\mathrm{m}路{\mathrm{s}}^{-1}}{589脳{10}^{-9}\mathrm{m}} \\ \mathrm{n}=10脳\frac{589脳{10}^{-9}}{6.626脳{10}^{-34}脳2.99脳{10}^8} \\ \mathrm{n}=2.973脳{10}^{19} \end{gathered}$$

The photons emitted from the sodium lamp spread in the form of a sphere around the lamp.

Determine the area of the eye from standing distance.

$\begin{array}{l}A=4{\mathrm{蟺谤}}^2\\ =4\mathrm{蟺}脳{\left(10m\right)}^2\\ =400{\mathrm{蟺尘}}^2\end{array}$

Determine the area of eye.

$$\begin{gathered} a=\mathrm{蟺}{\left(\mathrm{d}/2\right)}^2 \\ =\mathrm{蟺}脳{\left(\frac{4\mathrm{mm}}{2}\right)}^2 \\ =\mathrm{蟺}脳{\left(2\mathrm{mm}脳\frac{1脳{10}^{-3}\mathrm{m}}{1\mathrm{mm}}\right)}^2 \\ =4\mathrm{蟺}脳{10}^{-6}{\mathrm{m}}^2 \end{gathered}$$

Determine the number of photons incident on the eye.

$N=\frac{a}{A}n$

Substitute all the values in the above expression.

$$\begin{gathered} N=\frac{2.973脳{10}^{19}}{400蟺}脳4蟺脳{10}^{-6} \\ =2.973脳{10}^{11} \end{gathered}$$

Thus, the number of photons passing through an eye in 1s is $2.973脳{10}^{11}$.