Question

Calculate the linear momentum of photons of wavelength (a) 600 nm, (b) 70 pm, (c) 200 m.

Answer 1

Answer:

a) p = 1.10 * 10⁻²⁷ kg·m/s

b) p = 9.46 * 10⁻²⁴ kg·m/s

c) p = 3.31 * 10⁻³⁶ kg·m/s

Explanation:

To solve this problem we use the de Broglie's equation, which describes the wavelenght of a photon with its momentum:

λ=h/p

Where λ is the wavelength, h is Planck's constant (6.626 * 10⁻³⁴ J·s), and p is the linear momentum of the photon.

Rearrange the equation in order to solve for p:

p=h/λ

And now we proceed to calculate, keeping in mind the SI units:

a) 600 nm= 600 * 10⁻⁹ m

p=(6.626 * 10⁻³⁴ J·s) / (600*10⁻⁹m) = 1.10 * 10⁻²⁷ kg·m/s

b) 70 pm= 70 * 10⁻¹² m

p=(6.626 * 10⁻³⁴ J·s) / (70*10⁻¹²m) = 9.46 * 10⁻²⁴ kg·m/s

c) 200 m

p=(6.626 * 10⁻³⁴ J·s) / (200m) = 3.31 * 10⁻³⁶ kg·m/s