Question

Assuming rydberg constant to be 109670/cm,the longest wavelength line in the lyman series of the hydrogen spectrum is

Answer 1

The longest wavelength line in the Lyman series of the hydrogen spectrum is 1215.7A˚.

This can be calculated in the following ways:

• We know that, for Lyman series, n₁ = 1

• The wavelength can be calculated by the formula -

        1 / λ = R[ (1 / (n₁)²)− (1 / (n₂)²) ] x Z² where, R = Rydbergs constant   (109670/cm) and Z = atomic number

• As per the question, we have to find the longest wavelength and this implies that the energy difference in two states showing transition should be minimum, i.e., n₂=2.

• Thus, 1 / λ = R  [ (1 / 1²) − (1 / 2²) ]

                  1 / λ = 3 / 4 R

                      λ = 4 / 3 x 1 / R                          

                         = 1215.7A˚