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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3as107

Use $R_{H} = 1.097 \times 1 0^{7} m^{- 1}$ and $E_{1} = - 13.6 eV$ . Select the correct statements about the series limits of hydrogen.

AThe Paschen limit corresponds to a photon energy of $1.89 eV$
BThe Lyman limit lies near $91 nm$
CThe wavelengths of the Lyman, Balmer and Paschen limits are in the ratio $1 : 4 : 9$
DThe Balmer limit corresponds to a photon energy of $3.4 eV$

Answer: B, C, D

The limit is

1/ λ = R_{H} / n_{f}^{2}

, so

λ \propto n_{f}^{2} = 1 : 4 : 9

. Energies are

13.6/ n_{f}^{2}

:

3.4 eV

for Balmer and

1.51 eV

for Paschen (1.89 eV is the H-alpha line). The Lyman limit is

1/ R_{H} = 91.2 nm

.

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