You have 0.100 mol of H atoms in the ground state. How much energy is required to transition all of the atoms from the ground state to n=2?

Question

This also has a follow up questions after which is

What is the frequency of the light required to make this transition?

Answer 1

E = -2.179x10^-18 J (1/n_f² - 1/n_i²)

E = -2.179x10^-18 J (1/4 - 1/1)

E = -2.179x10^-18 J (-0.75)

E = 1.63x10^-18 J = energy for 1 electron

1.63x10^-18 J/e- x 6.02x10²⁸ electrons/mol x 0.1 mol = 9.8x10⁹ J = energy for 0.1 moles of electrons

Wavelength:

E = hν

ν = E/h = 1.63x10^-18 J/6.626x10^-34 Js

ν = 2.46x10¹⁵ s^-1 = 2.46x10¹⁵ Hz

Please check the math in both parts.