A beam of red light and a beam of violet light each deliver the same power on a surface. For which beam is the number of photons hitting the surface per second the greatest

The Planck's equation and the definition of power allow you to find the result for which beam has the largest number of photons is:

The energy of a photon is given by the Planck's equation.

          E = h f

Where h is the Planck constant and f the frequency.

The speed of light is related to wavelength and frequency.

           c = λ f

           f =

Let's  substitute

          E =  

Power is defined as energy per unit of time.

         P = W / t

         P t = W

The wavelength of red light, in the order of 700 nm, is greater than the wavelength of violet light, which is on the order of 400 nm, therefore the energy of a photon of red light is less than the energy of a photon of violet light.

The total energy deposited is the number of photons times the energy of each photons.  

         W =  

They indicate that the power delivered by the two rays is the same.

        #_ {red photons} d = #_{photons violet}    

The amount of energy of the violet photons is greater than the amount of energy of the red photons.

Consequently, to leave the same power, there must be more red photons than violet wavelength photons.

In conclusion, using Planck's equation and the definition of power, we can find the result for which beam has the greatest number of photons is:

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Options are;

(a) the red beam

(b) the violet beam

(c) it is the same for both beams

(d) cannot answer this without knowing the light intensity

A: Red Beam

Explanation:

The energy of a photon is given by the formula;

E = hc/λ

Where;

h is Planck's constant

c is speed of light

λ is wavelength

From online sources, wavelength of red light is greater than that of violet.

Thus, it means that the value of E for red light will be lesser than that of violet since the denominator under red light will be larger. Therefore, the beam of red light will have the greatest number of photons hitting the surface per second.