$v_{1}$ and $v_{2}$ are the frequencies series limit for Lyman and Blamer series. Which relation is correct for frequency $v_{3}$ of $I$ line of Lyman series?

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

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

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

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

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Solution

The correct option is A $v_{3} = v_{1} - v_{2}$

As we know,

$v = c R (1 / n_{1}^{2} - 1 / n_{2}^{2})$
For Lyman series limit, electron emits from infinte to first orbit so,
$: v_{1} = c R [\frac{1}{1^{2}} - \frac{1}{\infty^{2}}] = c R$ ......(i)
For Balmer series limit line, electron emits from infinite to second orbit so,
$: v_{2} = c R [\frac{1}{2^{2}} - \frac{1}{\infty^{2}}] = \frac{c R}{4}$ ......(ii)
Also,
For $I$ line of Lyman series, electron emits fron second orbit to first orbit and
$: v_{3} = c R [\frac{1}{1^{2}} - \frac{1}{2^{2}}] = \frac{3 c R}{4}$ .....(iii)
By (i),(ii) and (iii)
$v_{1} = v_{2} + v_{3}$
$∴ v_{3} = v_{1} - v_{2}$

Hence the correct option is B.

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v1 and v2 are the frequencies series limit for Lyman and Blamer series. Which relation is correct for frequency v3 of I line of Lyman series?

$v_{1}$ and $v_{2}$ are the frequencies series limit for Lyman and Blamer series. Which relation is correct for frequency $v_{3}$ of $I$ line of Lyman series?