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Question 19

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?

Answer

The expression for the energy of hydrogen of electron is

En = -2π2me4Z2/n2h2

Where m= mass of electrons

Z=atomic mass of atom

e = charge of electron

h = planck’s constant

When n = 1 then En = - (2.18X10-18 ) (GIVEN)

When n = 2 then En= - (2.18X10-18 )/4 = 0.5465X10-18 J

 

Therefore the energy required for ionization from n = 2 is 5.45 x 10-19 J

Now wavelength of light needed

= E=hv = hc

Or

λ = [{(6.62x10-24)(3x108)} / 5.45] x 10-19 = 3647

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