SATHEE: Atoms And Nuclei Question 55

Atoms And Nuclei Question 55

Question: The ratio of longest wavelength and the shortest wavelength observed in the five spectral series of emission spectrum of hydrogen is [MP PET 1999]

Options:

A) $\frac{4}{3}$

B) $\frac{525}{376}$

C) 25

D) $\frac{900}{11}$

Show Answer

Answer:

Correct Answer: D

Solution:

Shortest wavelength comes from
$\Rightarrow \frac{N}{10.38} = {(\frac{1}{2})}^{5} \Rightarrow N = 10.38 \times {(\frac{1}{2})}^{5}$ to $n_{2} = 1$

and longest wavelength comes from $n_{1} = 6$ to $n_{2} = 5$ in the given case.

Hence $\frac{1}{λ_{min}} = R, (\frac{1}{1^{2}} - \frac{1}{\infty^{2}}) = R$

$\frac{1}{λ_{max}} = R, (\frac{1}{5^{2}} - \frac{1}{6^{2}}) = R, (\frac{36 - 25}{25 \times 36}) = \frac{11}{900} R$
$∴ \frac{λ_{max}}{λ_{min}} = \frac{900}{11}$

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Atoms And Nuclei Question 55

Question: The ratio of longest wavelength and the shortest wavelength observed in the five spectral series of emission spectrum of hydrogen is [MP PET 1999]

Options:

Answer:

Solution:

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