Question

A 12.3 eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy level the hydrogen atoms would be excited? Calculate the wavelengths of the second member of Lyman series and second member of Balmer series.

Answer 1

 Let the hydrogen atoms be excited to nth energy level. 12.3=13.6112-1n2⇒12.3=13.6-13.6n2⇒13.6n2=13.6-12.3=1.3⇒n2=13.61.3⇒n≈3 The formula for calculating the wavelength of Lyman series is given below: 1λ=R1-1n2 For the second member of Lyman series: n = 3 ∴1λ=R1-132⇒1λ=1.09737×10789⇒λ=1025 A∘ The formula for calculating the wavelength of Balmer series is given below: 1λ=R14-1n2 For second member of Balmer series: n = 4 ∴1λ=R14-142⇒1λ=1.09737×107316⇒λ=4861 A∘