One way that scientists measure the mass of an unknown particle is to bounce a f

Question

One way that scientists measure the mass of an unknown particle is to bounce a familiar particle, such as a proton or electron, off the unknown particle in a bubble chamber. The initial and rebound velocities of the familiar particle is measured from photographs of the bubbles it creates as it moves; the information is used to determine the mass of the unknown particle.

(a) If a known particle of mass m and initial speed v0 collides elastically, head-on with a stationary unknown particle and then rebounds with speed v, find the mass of the unknown particle in terms of m, v, and v0.

(b) If the known particle is a proton and the unknown particle is a neutron, what will be the recoil speed of the proton and the final speed of the neutron?

Explanation / Answer

a)

Here , let the final speed of unknow particle is vf ,

and mass of unknow particle is mf ,

Now , using conservation of momentum ,

mf * vf - m * v = m*v0 ----(1)

Now , as the collision is elastic ,

v0 = v + vf

vf = v0 - v

mf *(v0 - v) = m (v + v0)

mf = m (v + v0)/(v0 - v)

the mass of unknow particle is m (v + v0)/(v0 - v)

b)

as the mass of proton = mass of neutron ,

mf = m

m = m (v + v0)/(v0 - v)

v0 - v = v + v0

v = 0 ,

Hence, final speed of proton is 0 m/s

and conservation of momentum ,

vn, f = v0

Hence ,

vp,f = 0 m/s

vn,f = v0

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