Question

A photon, a packet of electromagnetic radiation, carries both energy and momentum. Consider a photon with a wavelength of 670. nm in vacuum. What is the frequency of the photon?

What is the energy of the photon?

What is the momentum of the photon?

Answer 1

Solution:

The velocity of the photon in vacuum is c = 3*10⁸ m/s

Wavelength of the photon, λ = 670 nm

λ = (670nm)(1*10^-9 m/1nm)

λ = 670*10^-9 m

(a)

The frequency f of a photon is given by,

c = λ*f

f = c / λ

f = (3*10⁸ m/s)/(670*10^-9 m)

f = 4.48*10¹⁴ /s

f = 4.48*10¹⁴ Hz

(b)

The energy E of a photon is given by,

E =h*f                   (h = Planck's constant)

E = (6.63*10^-34 J.s)*(4.48*10¹⁴ /s)

E = 2.97*10^-19 J

E = (2.97*10^-19 J)*(1 eV / 1.602*10^-19J)

E = 1.85 eV

Thus the energy of the photon is 2.97*10^-19 J    (or 1.85 eV))

(c)

The momentum p of a photon is given by,

p = h/λ

p = (6.63*10^-34 J.s) / (670*10^-9 m)

p = 9.89*10^-28 kg.m/s