SATHEE: Modern Physics 1 Question 11

Modern Physics 1 Question 11

8. In a hydrogen like atom, when an electron jumps from the $M$ -shell to the $L$ -shell, the wavelength of emitted radiation is $λ$ . If an electron jumps from $N$ -shell to the $L$ -shell, the wavelength of emitted radiation will be (Main 2019, 11 Jan II)

(a) $\frac{27}{20} λ$

(b) $\frac{25}{16} λ$

(d) $\frac{16}{25} λ$

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Solution:

For hydrogen or hydrogen like atoms, we know that

$\frac{1}{λ} = R Z^{2} \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}$

where, $R$ is Rydberg constant and $Z$ is atomic number. When electron jumps from $M$ - shell to the $L$ - shell, then

$∴$ Eq (i) becomes

$\begin{aligned} n_{1} = 2 \\ n_{2} = 3 \end{aligned}$

(for $L$ - shell)

(for $M$ - shell)

$\frac{1}{λ} = R Z^{2} \frac{1}{2^{2}} - \frac{1}{3^{2}} = \frac{5}{36} R Z^{2}]$

Now, electron jumps from $N$ -shell to the $L$ - shell, for this

$\begin{array}{lr} n_{1} = 2 & (for L - shell) \\ n_{2} = 4 & (for N - shell) \end{array}$

$∴$ Eq. (i) becomes

$\frac{1}{λ^{'}} = R Z^{2} \frac{1}{2^{2}} - \frac{1}{4^{2}} = \frac{3}{16} R Z^{2}$

Now, we divide Eq (ii) by Eq (iii)

$\begin{aligned} \frac{λ^{'}}{λ} & = \frac{5}{36} R Z^{2} \div \frac{3}{16} R Z^{2} = \frac{20}{27} \\ or λ^{'} & = \frac{20}{27} λ \end{aligned}$

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Modern Physics 1 Question 11

8. In a hydrogen like atom, when an electron jumps from the $M$ -shell to the $L$ -shell, the wavelength of emitted radiation is $λ$ . If an electron jumps from $N$ -shell to the $L$ -shell, the wavelength of emitted radiation will be (Main 2019, 11 Jan II)

Solution:

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Modern Physics 1 Question 11

8. In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is λ. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be (Main 2019, 11 Jan II)

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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8. In a hydrogen like atom, when an electron jumps from the $M$ -shell to the $L$ -shell, the wavelength of emitted radiation is $λ$ . If an electron jumps from $N$ -shell to the $L$ -shell, the wavelength of emitted radiation will be (Main 2019, 11 Jan II)