Find the recoil velocity of the nucleus.

[looi76]

Homework Statement

An alpha particle is emitted from a stationary nucleus at $$1.8 \times 10^7 ms^{-1}$$.The mass of the particle is $$4u$$ and that of the nucleus is $$212u$$. (u is a unit of mass equal to $$1.66 \times 10^{-27}kg$$.)
(a) Find the recoil velocity of the nucleus.
(b) Explain how you know the direction of movement.

Homework Equations

Momentum before collision = Momentum after collision

The Attempt at a Solution

What does recoil velocity mean?

 

[alphysicist]

Hi looi76,

The recoil velocity of this nucleus is the velocity of the nucleus after the alpha particle is emitted. What do you get?

 

[Moetasim]

Recoil velocity refers to the velocity at which an object moves backwards or in the opposite direction after a collision or emission. In this case, it refers to the velocity at which the nucleus moves backwards after emitting an alpha particle. This is due to the conservation of momentum, which states that the total momentum of a system before and after a collision or emission must be equal.

To find the recoil velocity of the nucleus, we can use the equation for conservation of momentum:

Momentum before = Momentum after

Therefore, we can write:

(mass of alpha particle x initial velocity of alpha particle) = (mass of nucleus x recoil velocity of nucleus)

Solving for the recoil velocity of the nucleus, we get:

Recoil velocity of nucleus = (mass of alpha particle x initial velocity of alpha particle) / mass of nucleus

Substituting the given values, we get:

Recoil velocity of nucleus = (4u x 1.8 x 10^7 ms^-1) / 212u

= 3.4 x 10^5 ms^-1

Therefore, the recoil velocity of the nucleus is 3.4 x 10^5 ms^-1.

To determine the direction of movement, we can use the principle of conservation of momentum again. Since the alpha particle is emitted from the nucleus with a certain velocity, the nucleus will have an equal but opposite velocity in order to conserve momentum. This means that the nucleus will move in the opposite direction of the alpha particle, which is why we know the direction of movement of the nucleus.