Question

a proton of mass 1.66x10^-27 kg collides head on with a helium atom at rest.The helium atom has a mass of 6.64x10^-27 kg and recoils with a speed of 5x10^5 .If the collision is elastic what are the initial and final speeds of proton?

Answer 1

http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html#c1
(look at the last tableset at the bottom of the page) ;-)

Answer 2

Let the initial momentum of proton be \(P_1\) and final momentum of proton be \(P_2\). Let final momentum of Helium be \(P_3\).
From conservation of linear momentum, we have \(P_1=P_2+P_3\)
Also, KE is conserved during the process. So, \[\frac{P_1^2}{2m_p}=\frac{p_2^2}{2m_p} +\frac{P_3^2}{2m_{He}}\]\[\frac{P_2^2+P_3^2}{2m_p}=\frac{p_2^2}{2m_p} +\frac{P_3^2}{2m_{He}}\]Substitute values to get \(P_2\) That will give you final momentum of proton and that will give you final velocity of proton. A bit of further calculation will give you initial momentum of proton and initial velocity.

Answer 3

Sorry, in my above reply, I made a small mistake
It should be \[\frac{(P_2+P_3)^2}{2m_p}=\frac{P_2^2}{2m_p}+\frac{P_3^2}{2m_{He}}\]

Answer 4

Great explanation @ujjwal! :-D +1 medal