The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915 .The longest wavelength of spectral lines in the Balmar series will be ________

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Solution

Q.
The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915 $Å$ .The longest wavelength of spectral lines in the Balmar series will be ________ $Å$ . [2024]

Ans.
(6588) $\frac{h c}{λ} = - 13.6 (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

  Lyman series, shortest wavelength, highest energetic

   $\frac{h c}{λ_{0}} = - 13.6 \times 1$

  Balmer Series, $n_{1} = 2, n_{2} = 3$ (for longest wavelength)

   $\frac{h c}{λ_{1}} = - 13.6 (\frac{1}{2^{2}} - \frac{1}{3^{2}})$

$= - 13.6 \times \frac{5}{36}$

$λ_{1} = \frac{36}{5} \cdot λ_{0} = \frac{36}{5} \times 915 Å = 6588 Å$

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