Question

The photon energy for green light lies between the values for red and violet light. What is the approximate energy of the photons in green light? The intensity of sunlight above the Earth’s atmosphere is about 1400 W (J/s) per square meter. That is, when sunlight hits perpendicular to a square meter of area, about 1400 W of energy can be absorbed. Using the photon energy of green light, about how many photons per second strike an area of one square meter? (This is why the lumpiness of light was not noticed for so long.)

Short answer

The approximate energy of the photons of green light is$3.643\times {10}^{-19}\mathrm{J}$

$3.84\times {10}^{21}$ photons per second strike an area of one square meter.

Step-by-step solution

About Energy of photons and Definition of intensity of light

Energy of photons of light is defined as the energy carried by the photons and it is directly proportional to the light’s frequency.

The energy of a single photon is expressed as, $E=fh$where, $E$is Energy of a single photon, $f$is frequency of light and $6.626\times {10}^{-34}$Js is Planck’s constant.

Intensity of light is defined as power per unit area per unit time.

The intensity of sunlight falling on Earth’s surface is the energy received by the Earth’s curved surface area in one second.

Calculation of energy of photons of green light

Frequency of green light is$f=550\times {10}^{12}Hz.$

Substitute value of frequency and Planck’s constant into formula of energy of single photon.

$$\begin{gathered} E=550\times {10}^{12}\times 6.626\times {10}^{-34} \\ =3.643\times {10}^{-19}\mathrm{J} \end{gathered}$$

Therefore, the approximate energy of the photons of green light is$3.643\times {10}^{-19}$ .

Calculation of number of photons of green light

Given that, the intensity of sunlight above the Earth’s atmosphere is about $1400W$per square meter.

The formula for intensity of light is, $l=\frac{NE}{tA}$where $l$is intensity of light, N is number of photons, E is energy of single photon, t is time duration and A is area of the surface.

The number of photons falling on unit area in unit time is$N=\frac{ltA}{E}$

Substitute the values into the obtained formula to obtain the required number of photon.

$$\begin{gathered} \mathrm{N}=\frac{1400\mathrm{J}/{\mathrm{sm}}^2\times 1\mathrm{s}\times 1{\mathrm{m}}^2}{3.643\times {10}^{-19}\mathrm{J}} \\ =3.84\times {10}^{21} \end{gathered}$$

Thus, the approximate energy of the photons of green light is$3.643\times {10}^{-19}\mathrm{J}$ and$3.84\times {10}^{21}$ photons per second strike an area of one square meter.