The ratio of the frequencies of the long wavelength limits of the Balmer and Lyman series of hydrogen is

27 : 5

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5 : 27

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4 : 1

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1 : 4

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Solution

The correct option is D $27 : 5$
Longest wavelengths are formed when the electron falls from next highest orbit to the orbit of the series releasing the minimum amount of energy.
$E (B a l m e r) = K [1 - \frac{1}{4}] = \frac{3 k}{4}$ --------- (I)
$E (L y m a n) = K [\frac{1}{4} - \frac{1}{9}] = \frac{5 K}{36}$ ----------(II)
Ratio of (I) and (II),
Balmer : Lyman
$= \frac{3 K}{4} \times \frac{36}{5 K}$

$= 27 : 5$

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The ratio of the frequencies of the long wavelength limits of the Balmer and Lyman series of hydrogen is

The correct option is D 27:5Longest wavelengths are formed when the electron falls from next highest orbit to the orbit of the series releasing the minimum amount of energy.E(Balmer)=K[1−14]=3k4 --------- (I)E(Lyman)=K[14−19]=5K36----------(II)Ratio of (I) and (II),Balmer : Lyman=3K4×365K=27:5