JEE Main 2017 — Chemistry Physical Chemistry

2017mcqmedium

If the shortest wavelength in Lyman series of hydrogen atom is $A$ , then the longest wavelength in Paschen series of ${\mathrm{He}}^{+}$ is

Official previous-year question

Held on 8 Apr 2017 · Verified 6 Jul 2026.

Options

A
$\frac{5A}{9}$
B
$\frac{36A}{7}$
C
$\frac{36A}{5}$
D
$\frac{9A}{5}$

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Solution

$\frac{1}{\lambda }={R}_{H}\times {(Z)}^{2}(\frac{1}{{n}_{1}^{2}}-\frac{1}{{n}_{2}^{2}})$

Shortest wavelength for Lyman series of $H\mathrm{atom}$

${n}_{1}=1$ (Lyman series)

${n}_{2}=\infty$

SO, $\frac{1}{{\lambda }_{1}}=1\times {R}_{H}(\frac{1}{1}-\frac{1}{\infty })$

${\lambda }_{1}=\frac{1}{{R}_{H}}=A\therefore \lambda =A$

longest wavelength for Paschen series of ${\mathrm{He}}^{+}$ atom

${n}_{1}=3$

${n}_{2}=4$

$\frac{1}{{\lambda }_{2}}={(2)}^{2}\times {R}_{H}(\frac{1}{{(3)}^{2}}-\frac{1}{{(4)}^{2}})$

$\frac{1}{{\lambda }_{2}}=4\times {R}_{H}(\frac{7}{9\times 16})=\frac{R\times 7}{36}$

${\lambda }_{2}=\frac{36}{7{R}_{H}}=\frac{36}{7}A$ .

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Solution

$\frac{1}{\lambda }={R}_{H}\times {(Z)}^{2}(\frac{1}{{n}_{1}^{2}}-\frac{1}{{n}_{2}^{2}})$

Shortest wavelength for Lyman series of $H\mathrm{atom}$

${n}_{1}=1$ (Lyman series)

${n}_{2}=\infty$

SO, $\frac{1}{{\lambda }_{1}}=1\times {R}_{H}(\frac{1}{1}-\frac{1}{\infty })$

${\lambda }_{1}=\frac{1}{{R}_{H}}=A\therefore \lambda =A$

longest wavelength for Paschen series of ${\mathrm{He}}^{+}$ atom

${n}_{1}=3$

${n}_{2}=4$

$\frac{1}{{\lambda }_{2}}={(2)}^{2}\times {R}_{H}(\frac{1}{{(3)}^{2}}-\frac{1}{{(4)}^{2}})$

$\frac{1}{{\lambda }_{2}}=4\times {R}_{H}(\frac{7}{9\times 16})=\frac{R\times 7}{36}$

${\lambda }_{2}=\frac{36}{7{R}_{H}}=\frac{36}{7}A$ .

JEE Main 2017 — Chemistry Physical Chemistry

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Solution

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JEE Main 2017 — Chemistry Physical Chemistry

Options

Did you get this right?

Solution

Your note

JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

Keep practicing Physical Chemistry