Question

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

Answer 1

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