Consider a collision between an alpha particle (mass 4 amu) and an initially sta

Question

Consider a collision between an alpha particle (mass 4 amu) and an initially stationary oxygen nucleus (mass 16 amu). The oxygen nucleus is light enough that we cannot assume it is stationary after the collision. The initial and final velocities of the alpha particle and the oxygen nucleus (when they are far apart and no longer interacting) are shown below. The final speed of the oxygen nucleus is v2f = 1.20 Ý 105m/s.

(a) What was the initial speed of the alpha particle?

(b) What is the final speed of the alpha particle?

Explanation / Answer

let u1 aqnd u2 are initial velocities of alpha and oxygen respectievly....

and let v1 and v2 are the final velocities of alpha and oxygen respectievly...

then here given that u2=0

final speed of alpha is v1=(m1-m2)*u1/(m1+m2)........

final speed of oxygen is gven by v2=1.2*10^5 m/sec.....

but v2=2m1*u1/(m1+m2).....

u1=1.2(10^5)*(4+16)/4=6*10^5 m/s is the initial velocity of alpha.....................

final speed of alpha is v1=(4-16)*6*10^5/(4+16)=-3.6*10^5 m/sec i.e opposite to the initial direction

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