Atoms & Nuclei

JEE Main level, numerical answer, medium

119 of 239

Question 119 of 239

The ratio of wavelength of spectral lines Hα{H}_{\alpha } and Hβ{H}_{\beta } in the Balmer series is x20\dfrac{x}{20}. The value of xx is _____.

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Answer: 27

The formula to calculate the wavelength of Hα{H}_{\alpha }-line in Balmer series is given by
hcλα=13.6[14−19]...(1)\dfrac{hc}{{\lambda }_{\alpha }}=13.6\left[\dfrac{1}{4}-\dfrac{1}{9}\right]...\left(1\right)
The formula to calculate the wavelength of Hβ{H}_{\beta }-line in Balmer series is given by
hcλβ=13.6[14−116]...(2)\dfrac{hc}{{\lambda }_{\beta }}=13.6\left[\dfrac{1}{4}-\dfrac{1}{16}\right]...\left(2\right)
Divide equation (2) by equation (1)
⇒λαλβ=14−11614−19\Rightarrow \dfrac{{\lambda }_{\alpha }}{{\lambda }_{\beta }}=\dfrac{\dfrac{1}{4}-\dfrac{1}{16}}{\dfrac{1}{4}-\dfrac{1}{9}}
=3664×125=\dfrac{36}{64}\times \dfrac{12}{5}
=2720=\dfrac{27}{20}

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