An electron in a hydrogen atom relaxes to the n=4 level, emitting light of 74 THz.

Delta E = Ef - Ei

E = energy, h = plank constant, v = frequency

h = 6.626 * 10 ^-34 j*s, T = 10 ^ 12, v = 74 * 10 ^12 Hz, Hz = s^-1

E = (6.626 * 10^ - 34 j*s) (74 * 10 ^ 12 s^ - 1) = 4.90 * 10 ^ - 20 J

Delta E = Ef - Ei

-4.90 * 10 ^ - 20 J = - 2.18 * 10 ^ - 18J (1/4 ^2 - 1/x ^2)

0.0225 = 0.0625 - (1/x ^ 2)

0.225 - 0.0625 = - 1 / x ^ 2

- 0.0400 = - 1/x ^2 = - 1 / - 0.0400 = x^2

25 = x^2

x = 5