Question

A monoenergetic radiation beam is having a wavelength 0.5 micrometer. What is a energy of single photon in eV.

Answer 1

wavelength =0.5micrometer or 5*10-7m
we know that,
Energy=hc/wavelength
= 6.62*10-34×3*10+8/5*10-7
= 3.97*10-19 J
1Joule=6.62*10-18ev then,
3.97*10-19J =6.62*10-18×3.97*10-19
= 2.628ev
hope this will help you

Answer 2

The energy of the single photon is 2.484 eV.

Method I:

The wavelength of the mono energetic beam =  0.5 micrometer (μm)

                                                                           = 5000 A⁰ (Angstrom)

∵ 1 μm = 10⁻⁶ m

and, 1 A⁰ = 10⁻¹⁰ m

∴ 1 μm = 10⁴ A⁰

Now, we know, the most simple formula of calculating

The energy of a single photon = $\frac{12420}{Wavelength (in A)}$ eV

By putting the values, we get,

The energy of a single photon = 12420/5000 eV

                                                   = 2.484 eV

∴ The energy of a single photon  is 2.484 eV

Method II:

We know, the energy of a single photon, E = hc/λ

where h = Planck's constant

          c = speed of light

          λ = wavelength

Now, h = 6.62 × 10⁻³⁴ Js

         c = 3 × 10⁸ m/s

         λ = 0.5 micrometer  

            = 0.5 × 10⁻⁶  [∵ 1 μm = 10⁻⁶ m]

By putting these values in the above equation, we will get the value of E in Joule.

And 1 Joule = 6.242 × 10¹⁸ eV

As in the question we are asked to calculate it in eV, we have to multiply the value with 6.242 × 10¹⁸

We will get, the energy of single photon = 4.484 eV.