Answer:
Velocity of the helium nuleus = 1.44x10⁴m/s
Velocity of the proton = 2.16x10⁴m/s
Explanation:
From the conservation of linear momentum of the proton collision with the He nucleus:
(1)
<em>where : is the proton linear momentum initial,
: is the helium nucleus linear momentum initial,
: is the proton linear momentum final,
: is the helium nucleus linear momentum final </em>
<u>From (1):</u>
(2)
<em>where m₁ and m₂: are the proton and helium mass, respectively, and
: are the proton and helium nucleus velocities, respectively, before the collision, and
and
: are the proton and helium nucleus velocities, respectively, after the collision </em>
By conservation of energy, we have:
(3)
<em>where and
: are the kinetic energy for the proton and helium, respectively, before the colission, and
and
: are the kinetic energy for the proton and helium, respectively, after the colission </em>
<u>From (3):</u>
(4)
<u>Now we have two equations: (2) ad (4), and two incognits: and
. </u>
Solving equation (2) for , we have:
(5)
<u>From getting (5) into (4) we can obtain the :</u>
From solving the quadratic equation, we can calculate the velocity of the helium nucleus after the collision:
(6)
Now, by introducing (6) into (5) we get the proton velocity after the collision:
The negative sign means that the proton is moving in the opposite direction after the collision.
I hope it helps you!