In hydrogen like spectrum if wavelength of transition from 3rd to 2nd orbit is λ₁ then wavelength of transition from 4th to 3rd orbit (Bohr's) is λ₂. If λ₂/λ₁ = 20/x then value of x is (a) 5 (b) 6 (c) 7 (d) 8

Answer: (c). (1)/(λ) ∝ ((1)/(nf²)-(1)/(ni²)) 3→2: 14-19 = 5/36. 4→3: 19-116 = 7/144. (λ₂)/(λ₁) = (5/36)/(7/144) = 20/7 So x = 7, answer (c).

In hydrogen like spectrum if wavelength of transition from 3rd to 2nd… | MHT CET 2026 (15 May, Shift 2)

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Transitions, Photon Emission & Excitation

In hydrogen like spectrum if wavelength of transition from $3^{rd}$ to $2^{nd}$ orbit is $\lambda_{1}$ then wavelength of transition from $4^{th}$ to $3^{rd}$ orbit (Bohr's) is $\lambda_{2}$ . If $\lambda_{2}/\lambda_{1} = 20/x$ then value of $x$ is

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Answer: (c)

$\frac{1}{\lambda} \propto \left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$
$3\to2$ : $\frac14-\frac19 = \frac{5}{36}$ . $4\to3$ : $\frac19-\frac1{16} = \frac{7}{144}$ .
$\frac{\lambda_2}{\lambda_1} = \frac{5/36}{7/144} = \frac{20}{7}$
So $x = 7$ , answer (c).

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