Particles after an elastic collision

[Suyash Singh]

Homework Statement

A particle A of mass m and initial velocity v collides with a particle B of mass m 2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λA to λB after the collision is

Homework Equations

u initial velocity
v final velocity

The Attempt at a Solution

after collision
A->V-x
B->x
λA/λB=(h/m(v-x)) / (h/( m/2 x)) = 1/2x/v-x

momentum conservation--
mv=m(v-x)+ m/2(x)
v=v-x+x/2

x=0 !

now what??
I really don't understand anything and all sites do different solutions so please don't put my question in black hole.

 

[drvrm]

Homework Statement

A particle A of mass m and initial velocity v collides with a particle B of mass m 2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λA to λB after the collision is

Homework Equations

u initial velocity
v final velocity

The Attempt at a Solution

after collision
A->V-x
B->x
λA/λB=(h/m(v-x)) / (h/( m/2 x)) = 1/2x/v-x

momentum conservation--
mv=m(v-x)+ m/2(x)
v=v-x+x/2

x=0 !

now what??
I really don't understand anything and all sites do different solutions so please don't put my question in black hole.

you are doing elastic collision
so the momentum and energy both will be conserved.
write down energy before the collision and after the collision and equate them
similarly for momentum ...before and after will be equal

solve for velocities of the two particles after collision. and then write down the wavelength = h/momentum and take ratio.

 

[neilparker62]

For perfectly elastic collisions you can use the formula Δp = 2μΔv where μ is the reduced mass [ m1 * m2 /(m1 + m2) ] of the colliding objects and Δv is their relative velocity. Then momentum of stationary object after collision will be Δp and of moving object p(before) - Δp. Convert to wavelengths using the normal formula.