An electron in the n=6 level of the hydrogen atom relaxes to a lower energy level, emitting light of ? =93.8nm. find the principal level to which the electron relaxed.

We can find the principal level or lower level using Rydberg's formula:

1/w = R(1/L² - 1/U²) 

where:

w is the wavelength (93.8 nm),

L is the lower energy level (unknown)

U the upper energy level (n= 6)

R is Rydberg's constant (10,967,758 waves per meter)

Substituing known values into the equation:
1/(9.38 * 10^-8 m.) = 10,967,758(1/L² - 1-36)

Using the solver function of the calculator to get for L:

L = 0.999 
so L = 1. 
The lower level is 1 (the ground state).