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**Hint:**The energy flux of sunlight is the power of sunlight reaching the surface of the earth per ${m^2}$.

Power can also be written as the product of energy of each photon and the total number of photons.$P = nE$

Energy of photon,$E$ is given by the equation

$E = h\upsilon $

Where, $\upsilon $ is the frequency and $h$ is the Planck’s constant.

The value of Planck’s constant is

\[h = 6.626 \times {10^{ - 34}}\,{m^2}kg{s^{ - 1}}\]

We know $c = \upsilon \lambda $

Where, $c$ is the speed of light and $\lambda $ is the wavelength.

Therefore,

$\upsilon = \dfrac{c}{\lambda }$

**Complete step by step solution:**

The energy flux of sunlight or the power of sunlight reaching the surface of the earth per ${m^2}$ is $\phi = 1.388 \times {10^3} W/{{m^2}}$.

That is power, $P = 1.388 \times {10^3}\,W$

Average wavelength,

$

\lambda = 550\,nm \\

= 550 \times {10^{ - 9}}\,m \\

$.

We need to find the number of photons per square meter that are incident on the Earth per second.

Let this number be $n$ .

Power can also be written as the product of energy of each photon and the total number of photons.$P = nE$

Energy of photon,$E$ is given by the equation

$E = h\upsilon $...........….. (1)

Where, $\upsilon $ is the frequency and $h$ is the Planck’s constant.

The value of Planck’s constant is

\[h = 6.626 \times {10^{ - 34}}\,{m^2}kg{s^{ - 1}}\]

In the question the wavelength of the photon is given. Hence, we need to write equation (1) in terms of wavelength.

We know $c = \upsilon \lambda $

Where, $c$ is the speed of light.

Therefore,

$\upsilon = \dfrac{c}{\lambda }$..........……(2)

Substitute equation (2) in equation (1). We get

$E = h\dfrac{c}{\lambda }$

Therefore,

$

P = nE \\

= nh\dfrac{c}{\lambda } \\

$

We need to find $n$

That is,

$n = \dfrac{{P\lambda }}{{hc}}$

Now, substitute the given values.

$

n = \dfrac{{1.388 \times {{10}^3}\, \times 550 \times {{10}^{ - 9}}\,}}{{6.626 \times {{10}^{ - 34}}\, \times 3 \times {{10}^8}}} \\

= 3.847 \times {10^{21}}\, \\

$

So, the number of photons per square meter that are incident on the Earth per second is $3.847 \times {10^{21}}\,$.

**Note:**Formulae to remember-

$P = nE$

Where, $n$ is the number of photons and $E$ is the energy of each photon.

$E = h\upsilon $

Where, $\upsilon $ is the frequency and $h$ is the Planck’s constant

$c = \upsilon \lambda $

Where, $c$ is the speed of light, $\upsilon $ is the frequency and $\lambda $ is the wavelength.

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