The electron energy in hydrogen atom is given by En= (–2.18 × 10–18)/n2J. 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?
Given:
Electron energy in Hydrogen atom En = [(–2.18 × 10–18)/n2] J
Energy for first state, E1 = [–2.18 × 10–18]/12
= –2.18 × 10–18 J
Energy for second state, E2 = [–2.18 × 10–18]/22
= –0.5465 × 10–18 J
By Planck’s relation we have,
Energy, E = h×v
But we know v = [c] / [λ]
Where
c = Speed of Light
v= Frequency
λ = Wavelength
So, E = hc /λ
λ = hc / E
= [[6.626×10-34] × [3×108]] / [0.5465 × 10–18]
= [1.9878×10-25] / [0.5465 × 10–18]
= 3.637×10-7 m
Therefore, the wavelength is 3.64×10-7 m