Question

The electron energy in hydrogen atom is given by E_n = {(-2.18 x 10^-18)}/{n²} J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Answer 1

E_n = {-2.18 x 10^-18}/{n²} J

Energy required to remove an electron from n = 2 is

ΔE = E_∞ - E₂

Energy is related to the wavelength through the relationship

ΔE = hc/λ

or, λ = hc/ΔE

= {6.626 x 10^-34 Js x 3 x 10⁸ ms^-1}/{5.42 x 10^-19 J}

λ = 3.647 x 10^-7 m

= 3.647 x 10^-5 cm

Thus, the wavelength of the light that can be used to cause this transition is 3.647 x 10^-5 cm (or 3647 Å)