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Q.

$v_{1} and v_{2}$ are the frequencies series limit for lyman and Balmer series. Which relation is correct for frequency v₃ of I line of Lyman series?

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a

$v_{3} = \frac{v_{1}}{v_{2}}$

b

$v_{3} = v_{1} \times v_{2}$

c

$v_{3} = v_{1} + v_{2}$

d

$v_{3} = V_{1} - V_{2}$

answer is B.

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Detailed Solution

$ν = \frac{∆ E}{h}; Let, ∆ E = E_{1} (H) (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) = x (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) ν_{1} = ν_{\propto \to 1} = \frac{1}{h} x (\frac{1}{1^{2}} - \frac{1}{\propto}) = \frac{x}{h} ν_{2} = ν_{\propto \to 2} = \frac{1}{h} x (\frac{1}{2^{2}} - \frac{1}{\propto}) = \frac{x}{4 h} ν_{3} = ν_{2 \to 1} = \frac{1}{h} x (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = \frac{3 x}{4 h} ∴ ν_{3} = ν_{1} - ν_{2}$

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