Particle <math><mi>A</mi></math> of mass <math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mi>A</mi></mrow></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math> moving along the <math><mi>x</mi></math> -axis with velocity <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math> collides elastically with another particle <math><mi>B</mi></math> at rest having mass <math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mi>B</mi></mrow></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math> . If both particles move along the <math><mi>x</mi></math> axis after the collision, the change <math><mi mathvariant="normal">Δ</mi><mi>λ</mi></math> in de-Broglie wavelength of particle <math><mi>A</mi></math> , in terms of its de-Broglie wavelength <math><mfenced separators="|"><mrow><mrow><msub><mrow><mrow><mi>λ</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfenced></math> before collision is:

Sol. ⇒V?1=2Ucm?-U1?⇒2m/2Vom2+m3-Vo⇒65Vo-Vo⇒V05⇒λo=hcm2Voλf=hcM2Vo5⇒Δλ=8hcmVo

Particle&nbsp;<math><mi>A</mi></math>&nbsp;of mass&nbsp;<math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mi>A</mi></mrow></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math>&nbsp;moving along the&nbsp;<math><mi>x</mi></math>&nbsp;-axis with velocity&nbsp;<math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math>&nbsp;collides elastically with another particle&nbsp;<math><mi>B</mi></math>&nbsp;at rest having mass&nbsp;<math><msub><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mi>B</mi></mrow></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math>&nbsp;. If both particles move along the&nbsp;<math><mi>x</mi></math>&nbsp;axis after the collision, the change&nbsp;<math><mi mathvariant="normal">Δ</mi><mi>λ</mi></math>&nbsp;in de-Broglie wavelength of particle&nbsp;<math><mi>A</mi></math>&nbsp;, in terms of its de-Broglie wavelength&nbsp;<math><mfenced separators="|"><mrow><mrow><msub><mrow><mrow><mi>λ</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfenced></math>&nbsp;before collision is:

Ask & Answer Question

Physics Class 12th Units and Measurements physics ncert exemplar solutions class 12th chapter two

Particle $A$ of mass $m_{A} = \frac{m}{2}$ moving along the $x$ -axis with velocity $v_{0}$ collides elastically with another particle $B$ at rest having mass $m_{B} = \frac{m}{3}$ . If both particles move along the $x$ axis after the collision, the change $Δ λ$ in de-Broglie wavelength of particle $A$ , in terms of its de-Broglie wavelength $(λ_{0})$ before collision is:

Option 1 -

$Δ λ = \frac{3}{2} λ_{0}$

Option 2 -

$Δ λ = \frac{5}{2} λ_{0}$

Option 3 -

$Δ λ = 2 λ_{0}$

Option 4 -

$Δ λ = 4 λ_{0}$

5 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

Sol. $\Rightarrow {\overset{?}{V}}_{1} = 2 \overset{?}{U_{c m}} - \overset{?}{U_{1}} \Rightarrow 2 [\frac{m / 2 V_{o}}{\frac{m}{2} + \frac{m}{3}}] - V_{o}$

$\Rightarrow \frac{6}{5} V_{o} - V_{o} \Rightarrow \frac{V_{0}}{5}$

$\Rightarrow λ_{o} = \frac{h c}{(\frac{m}{2} V_{o})} λ_{f} = \frac{h c}{(\frac{M}{2} \frac{V_{o}}{5})}$

$\Rightarrow Δ λ = \frac{8 h c}{{m V}_{o}}$

0 Upvotes 0 Downvotes

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question