Q. In hydrogen atom, which one of the following transitions produce a spectrum line of maximum wavelength?

Solution:

For hydrogen atom spectrum,
$\dfrac{1}{\lambda} =R \left(\dfrac{1}{n_{f}^{2}} -\dfrac{1}{n_{i}^{2}}\right)$
Therefore, for $ \ce{6 \, to\, 5; \lambda = \dfrac{30}{R}}$
for $ \ce{5 \, to\, 2; \lambda = \dfrac{10}{3R}}$
for $ \ce{4 \, to\, 1; \lambda = \dfrac{16}{15R}}$
for $ \ce{2 \, to\, 1; \lambda = \dfrac{4}{3R}}$
Hence, wavelength is maximum for transition 6 to 5.

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