What quantum number is associated with a hydrogen atom orbital that has an energy of −2.420 x 10−19 J?

Question

What quantum number is associated a hydrogen atom orbital that has an energy of −4.445 x 10−20 J?

Answer 1

The energy of level n equals -13.6 eV/n^2.
As 1 eV equal 1.602 x 10^-19 J we have
n^2 = -13.6 x 1.602 x 10^-19 / −2.420 x 10−19 = 9 => n=3
and
n^2 = -13.6 x 1.602 x 10^-19 / −4.445 x 10−20 = 49 => n=7

Answer 2

The equation to use is:

E = - (Rhc)/nexp2

R = 1.097 x 10exp7/m
h= 6.63 x 10exp-34J*s
c= 3.0 x 10exp8 m/s

Using the first energy, nexp2 = 49, thus n = 7
The second energy, nexp2 = 49, thus n = 7 also