The electron energy in hydrogen atom is given by En = (-2.18 × 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?

Question 2.19: The electron energy in hydrogen atom is given by E_n = (-2.18 × 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
Given,

Energy required for ionization from n = 2 is given by,

= 0.545 × 10^-18 J
ΔE = 5.45 × 10^-19 J

Here, λ is the longest wavelength causing the transition.

= 3647 × 10^-10 m
= 3647 Å