Question

What is the wavenumber and wavelength of the first transition in the Lyman, Balmer and Paschen series in the atomic spectra of hydrogen?

Answer 1

Lyman series first transition means 2 to 1 transition

We know $v^{-}=1/\lambda =R[1/n_1^2-1/n_2^2]$

$v^{-}=1.09737\times {10}^7[1/1^2-1/2^2]$

$v^{-}=8.23\times {10}^6$

$\lambda =1.21\times {10}^{-}7$

Balmer series first transition means 3 to 2 transition

We know $v^{-}=1/\lambda =R[1/n_1^2-1/n_2^2]$

$v^{-}=1.09737\times {10}^7[1/2^2-1/3^2]$

$v^{-}=1.53\times {10}^6$

$\lambda =6.5\times {10}^{-}7$

Paschen series first transition means 4 to 3 transition

We know $v^{-}=1/\lambda =R[1/n_1^2-1/n_2^2]$

$v^{-}=1.09737\times {10}^7[1/3^2-1/4^2]$

$v^{-}=6.09\times {10}^5$

$\lambda =1.64\times {10}^{-}6$