SATHEE: Modern Physics 4 Question 3

Modern Physics 4 Question 3

3. Two particles move at right angle to each other. Their de-Broglie wavelengths are $λ_{1}$ and $λ_{2}$ , respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $λ$ of the final particle, is given by

(a) $\frac{1}{λ^{2}} = \frac{1}{λ_{1}^{2}} + \frac{1}{λ_{2}^{2}}$

(Main 2019, 8 April I)

(b) $λ = \sqrt{λ_{1} λ_{2}}$

(d) $\frac{2}{λ} = \frac{1}{λ_{1}} + \frac{1}{λ_{2}}$

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Solution:

Given, de-Broglie wavelengths for particles are $λ_{1}$ and $λ_{2}$ .

So, $λ_{1} = \frac{h}{p_{1}}$ and $λ_{2} = \frac{h}{p_{2}}$

and momentum of particles are

$p_{1} = \frac{h}{λ_{1}} and p_{2} = \frac{h}{λ_{2}}$

Given that, particles are moving perpendicular to each other and collide inelastically.

So, they move as a single particle.

So, by conservation of momentum and vector addition law, net momentum after collision,

$p_{net} = \sqrt{p_{1}^{2} + p_{2}^{2} + 2 p_{1} p_{2} \cos 90^{\circ}} = \sqrt{p_{1}^{2} + p_{2}^{2}}$

Since,

$p_{1} = \frac{h}{λ_{1}} and p_{2} = \frac{h}{λ_{2}}$

$So, p_{net} = \sqrt{\frac{h^{2}}{λ_{1}^{2}} + \frac{h^{2}}{λ_{2}^{2}}}$

Let the de-Broglie wavelength after the collision is $λ_{net}$ , then

$p_{net} = \frac{h}{λ_{net}}$

From Eqs. (i) and (ii), we get

$\frac{h}{λ_{net}} = \sqrt{\frac{h^{2}}{λ_{1}^{2}} + \frac{h^{2}}{λ_{2}^{2}}} \Rightarrow \frac{1}{λ_{net}^{2}} = \frac{1}{λ_{1}^{2}} + \frac{1}{λ_{2}^{2}}$

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Modern Physics 4 Question 3

3. Two particles move at right angle to each other. Their de-Broglie wavelengths are $λ_{1}$ and $λ_{2}$ , respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $λ$ of the final particle, is given by

Solution:

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चिकित्सा तैयारी

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Modern Physics 4 Question 3

3. Two particles move at right angle to each other. Their de-Broglie wavelengths are λ1 and λ2, respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength λ of the final particle, is given by

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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3. Two particles move at right angle to each other. Their de-Broglie wavelengths are $λ_{1}$ and $λ_{2}$ , respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $λ$ of the final particle, is given by