A particle 'A' of mass 'm' moving with an initial velocity 'v' collides elastically with a particle B of mass 2m which is initially at rest. The ratio of the de-Broglie wavelengths (((λ )A/(λ )B)) of the particles A and B after collision is

Question

A particle 'A' of mass 'm' moving with an initial velocity 'v' collides elastically with a particle B of mass 2m which is initially at rest. The ratio of the de-Broglie wavelengths (((λ )A/(λ )B)) of the particles A and B after collision is (A) 2 (B) 3 (C) 8 (D) 4

Tardigrade Admin · Accepted Answer

From Conservation of momentum mv+0=mv1+2mv2 v=v1+2v2 ldots (i) coefficient of restitution; e=(v2 - v1/v) v2-v1=v...(ii) from (i) and (ii) ; v2=(2 v/3),v1=-(v/3) (λ A/λ B)=(2 m v2/m v1)=(2 v2/v1)=4 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-ry8pxrx2lcx45ov3.jpg" />

Q. A particle $^{'} A^{'}$ of mass $^{'} m^{'}$ moving with an initial velocity $^{'} v^{'}$ collides elastically with a particle $B$ of mass $2 m$ which is initially at rest. The ratio of the de-Broglie wavelengths $(\frac{( λ ) _{A}}{( λ ) _{B}})$ of the particles $A$ and $B$ after collision is

$2$

$3$

$8$

$4$

Q. A particle ′A′ of mass ′m′ moving with an initial velocity ′v′ collides elastically with a particle B of mass 2m which is initially at rest. The ratio of the de-Broglie wavelengths ((λ)B​(λ)A​​) of the particles A and B after collision is

2

3

8

4

From Conservation of momentum mv+0=mv1​+2mv2​ v=v1​+2v2​…(i) coefficient of restitution; e=vv2​−v1​​ v2​−v1​=v...(ii) from (i) and (ii) ; v2​=32v​,v1​=−3v​ λB​λA​​=mv1​2mv2​​=v1​2v2​​=4

Q. A particle $^{'} A^{'}$ of mass $^{'} m^{'}$ moving with an initial velocity $^{'} v^{'}$ collides elastically with a particle $B$ of mass $2 m$ which is initially at rest. The ratio of the de-Broglie wavelengths $(\frac{( λ ) _{A}}{( λ ) _{B}})$ of the particles $A$ and $B$ after collision is

$2$

$3$

$8$

$4$