Knowing that the length of electromagnetic radiation is 5.5 ∙ 10-7 m, find the frequency; photon energy

Given:

λ = 5.5 * 10 ^ (- 7) m;

h = 6.63 * 10 ^ (- 34) J * s;

s = 300,000 km / s = 300,000,000 m / s = 3 * 10 ^ 8 m / s.

To find:

v -?;

E -?.

Solution:

We use the formula E = (h * c) / λ, E is the photon energy, v is the frequency.

E = (6.63 * 10 ^ (- 34) J * s * 3 * 10 ^ 8 m / s) / (5.5 * 10 ^ (- 7) m) = 6.63 * 3 / 5.5 * 10 ^ (- 34 + 8 – (-7)) J = 3.62 * 10 ^ (- 19) J.

We use the formula c = λ * v. Hence, v = c / λ.

v = (3 * 10 ^ 8 m / s) / (5.5 * 10 ^ (- 7) m) = 3 / 5.5 * 10 ^ (8 – (-7)) Hz = 0.55 * 10 ^ 15 Hz.

Answer: v = 0.55 * 10 ^ 15 Hz and E = 3.62 * 10 ^ (- 19) J.