The transition from ni = 4 to an energy level with nf = 2, will give rise to a spectral line of the Balmer series. The energy involved in the transition is given by the relation,
Solving the equation we get,
E = 2.18 × 10-18 [(1/42) - (1/22)]
= 2.18 × 10-18 [1-4/16)]
= 2.18 × 1018 [-3/16]
or, E = -(4.0875 × 10-19 J)
The negative sign indicates that the energy is emitted during the transition. Now, the wavelength of transmission is given by the expression,
λ = hc/E
where c = velocity of light in vaccum = 3 × 108 m/s
h = Planck’s constant = 6.626 × 10-34 J sec
Substituting the values we get,
λ = (6626 × 10-34) (3 × 108) / (-40875 × 10-19)
= 486 × 107m
or, λ = 486 nm
