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

We can find the lower level by using Rydberg's formula: 1/w = R (1/L² - 1/U²) where:

w - wavelength (9.38nm),

L - lower energy level

U - upper energy level (6); and

R - Rydberg's constant (10,967,758 waves per meter for hydrogen).

So plugging in the information above:

1 / (9.38 * 10**-8 m.) = 10,967,758 (1/L² - 1-36)

But we need to solve for L.

The left side (1/9.38 * 10**-8) becomes 10,660,980

So translating:

10660980 = 10967758 (1/L² - 0.02777777)

Then divide both sides by 10967758

we get: 0.9720291 = 1/L² - 0.02777777.

then add 0.02777777 to both sides

we get: 0.9998 = 1/L²

0.9998 is very close to 1, so we can approximate 1/L² = 1 so L = 1.

Therefore the lower level is 1 which is the ground state.