Dear student
We have the relation λ = h/mv,
where m = 9.1 x 10-31 kg, is the mass of the electron,
h = 6.6 x 10-34 J.s, is the Planck's constant
v the velocity of the electron.
Since kinetic energy E = ½mv2, we can write mv = √(2mE) ⇒ E = h2/(2mλ2)
We have for hydrogen atom, IEI = 13.6/n2, where n is the principal quantum number.
13.6/n2 = h2/(2mλ2)
= (6.6 x 10-34 J.s)2/(2 x 9.1 x 10-31 kg x 10-9x2 m)
This gives n = 2.99 ? 3
