The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly ______ nm. [2026]

Question

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly ______ nm. [2026]

Smart Achievers · Accepted Answer

(1)

$n = 4$ ___________________

$n = 3$ ___________________ $Paschen$

$n = 2$ ___________________ $Balmer$

$n = 1$ ___________________ $Lyman$

$Smallest wavelength of Lyman$

$\frac{1}{λ} = R (\frac{1}{1^{2}} - \frac{1}{\infty^{2}})$

$R = \frac{1}{λ} = \frac{1}{91} {nm}^{- 1}$

$λ_{\max}$ for Balmer series

$n_{1} = 2 \to n_{2} = 3$

$\frac{1}{λ_{B}} = R (\frac{1}{4} - \frac{1}{9})$

$\frac{1}{λ_{B}} = \frac{1}{91} (\frac{5}{36})$

$λ_{B} = (\frac{91 \times 36}{5}) = 655.2 nm$

$λ_{\max}$ Paschen

$n_{1} = 3 \to n_{2} = 4$

$\frac{1}{λ_{p}} = \frac{1}{91} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = \frac{1}{91} (\frac{7}{144})$

$λ_{p} = (\frac{91 \times 144}{7}) = 1872 nm$

$Δ λ = λ_{p} - λ_{B}$

$Δ λ = 1872 - 655.2$

$Δ λ = 1216.8$

$Δ λ \approx 1217$

Solution

Q.
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly ______ nm. [2026]

1 1217

2 1550

3 1784

4 1875

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