Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from n = 5 to n = 1 .

Answer 1

1/λ = 1.097x10⁷m^-1 (1/n_f² - 1n_i²)

λ = wavelength = ?

n_f = final energy level = 1

n_i = initial energy level = 5

1/λ = 1.097x10⁷m^-1 (1/1 - 1/25) = 1.097x10⁷m^-1 (0.96)

1/λ = 1.05x10⁷m^-1

λ = 9.5x10^-8 m

E = hc/λ

E = energy = ?

h = Plank's constant = 6.626x10^-34 Jsec

c = speed of light = 3x10⁸ ms^-1

λ = 9.5x10^-8 m

E = (6.626x10^-34 Jsec)(3x10⁸ msec^-1)/9.5x10^-8 m)

E = 2.09x10^-18 J