Calculate the energy required to ionize a hydrogen atom to an excited state where the electron is initially in the n = 5 energy level. Report your answer in kilojoules. ΔΕ = ?

Answer 1

We can use Rydberg equation:

∆E = -R_H (1/n_f² - 1/n_i²⁾

∆E = ?

RH = 2.179x10-18 J

nf = final energy level = ∞

ni = initial energy level = 5

∆E = -2.179x10^-18 J (0 - 1/25) = + 8.716x10^-20 J

∆E = 8.716x10^-20 J x 1 kJ/1000 J = 8.716x10^-23 kJ (sign is positive as energy is absorbed)

E = hc/λ

E = energy = 8.716x10^-20 J

h = Planck's constant = 6.626x10^-34 J-sec

c = speed of light = ~3x108 m/sec

λ = wavelength = ?

λ = hc/E = (6.626x10^-34Jsec)(3x10⁸ m/sec) / 8.716x10^-20 J

λ = 2.28x10^-6 m x 1x10⁹ nm/m = 2.28x10³ nm = 2280 nm