The hydrogen spectrum consists of several spectral lines in the Lyman series (; has the lowest energy among the Lyman series). Similarly, it consists of several spectral lines in the Balmer series (; has the lowest energy among the Balmer lines). The en

Question

The hydrogen spectrum consists of several spectral lines in the Lyman series ( $L_{1}, L_{2}, L_{3}, \dots$ ; $L_{1}$ has the lowest energy among the Lyman series). Similarly, it consists of several spectral lines in the Balmer series ( $B_{1}, B_{2}, B_{3}, \dots$ ; $B_{1}$ has the lowest energy among the Balmer lines). The energy of $L_{1}$ is $x$ times the energy of $B_{1}$ . The value of $x$ is _______ $\times 10^{- 1}$ . (Nearest integer) [2026]

Smart Achievers · Accepted Answer

(54)

$Δ E (L_{1}) = 13.6 Z^{2} (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = 13.6 Z^{2} \times \frac{3}{4}$

$x$

$\frac{Δ E (L_{1})}{Δ E (B_{1})} = \frac{3}{5} \times 9 = \frac{27}{5} = x$

$x = (\frac{27}{5} \times 10) \times 10^{- 1} = 54 \times 10^{- 1}$

Solution

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Solution

Ans. (54) ΔE(L1)=13.6 Z2(112-122)=13.6 Z2×34 ΔE(B1)=13.6 Z2(122-132)=13.6 Z2×54×9 ΔE(L1)ΔE(B1)=35×9=275=x x=(275×10)×10-1=54×10-1

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