Question

What is the wavelength of light that can cause a transition of an electron in the hydrogen atom from the orbit with n = 2 to n = 9?

Answer 1

The energy of the hydrogen atom can be written as, E_n = -13.6/n² eV
Change in energy, E = E₉ - E₂
= -13.6 [1/9² - 1/2²]
= 3.23 eV
= 3.23 * 1.60 * 10^-16 J
= 5.17 * 10^-16 J

E = hc/
= hc/(E)
= [6.63 * 10^-34 * 3.00 * 10⁸] / [5.17 * 10^-16]
= 3.85 * 10^-10 m