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Question: Let \(\upsilon\)<!-- -->1 be the frequency of the series limit of the Lyman series, \(\upsilon\)<!--...

Let υ\upsilon1 be the frequency of the series limit of the Lyman series, υ\upsilon2 be the frequency of the first line of the Lyman series, and υ\upsilon3 be the frequency of the series limit of the Balmer series :

A

υ1−υ2=υ3\upsilon_{1} - \upsilon_{2} = \upsilon_{3}

B

υ2−υ1=υ3\upsilon_{2} - \upsilon_{1} = \upsilon_{3}

C

υ3=1/2(υ1−υ3)\upsilon_{3} = 1/2\left( \upsilon_{1} - \upsilon_{3} \right)

D

υ1+υ2=υ3\upsilon_{1} + \upsilon_{2} = \upsilon_{3}

Answer

υ1−υ2=υ3\upsilon_{1} - \upsilon_{2} = \upsilon_{3}

Explanation

Solution

v=RCZ2(1n12−1n22)v = RCZ^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right).

}}{\mathbf{v}_{\mathbf{2}}\mathbf{= RC}\mathbf{Z}^{\mathbf{2}}\left( \frac{\mathbf{1}}{\mathbf{1}^{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{\mathbf{2}^{\mathbf{2}}} \right)\mathbf{= RC}\mathbf{Z}^{\mathbf{2}}\mathbf{.}}$$ $${v_{3} = RCZ^{2}\left( \frac{1}{2^{2}} - \frac{1}{\infty^{2}} \right) = RCZ^{2}. }{\therefore \upsilon_{1} - \upsilon_{2} = \upsilon_{3}.}$$