The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is : [2026]

Question

The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is : [2026]

Smart Achievers · Accepted Answer

(1)

$Transition of first Balmer line$

$n_{1} = 2; n_{2} = 3$

$Δ E = x = 13.6 {(1)}^{2} [\frac{1}{2^{2}} - \frac{1}{3^{2}}] . . . . . . . . . . (i)$

$Transition of 2nd Balmer line$

$n_{1} = 2; n_{2} = 4$

$Δ E = 13.6 {(1)}^{2} [\frac{1}{2^{2}} - \frac{1}{4^{2}}] . . . . . . . . . . (i i)$

$Divide Eq. (ii) by Eq. (i)$

$\frac{Δ E}{x} = \frac{\frac{1}{4} - \frac{1}{16}}{\frac{1}{4} - \frac{1}{9}}$

$\frac{Δ E}{x} = \frac{\frac{3}{16}}{\frac{5}{36}}$

$\frac{Δ E}{x} = \frac{27}{20}$

$Δ E = 1.35 x$

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