# Elastic collision between alpha particle and gold Nuclei

• xoxomae
In summary, when an alpha particle collides elastically with a nucleus, the nucleus recoils and the alpha particle rebounds. The kinetic energy of the recoiling nucleus is equal to the initial kinetic energy of the alpha particle, while the rebounding alpha particle has a final kinetic energy of 3.94 MeV. The conservation of momentum is used to find the recoil velocities of the particles, and then the kinetic energies can be calculated using the masses of the particles.
xoxomae

## Homework Statement

When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 3.94 MeV alpha particle has a head-on elastic collision with a gold nucleus that is initially at rest. What is the kinetic energy of (a) the recoiling nucleus and (b) the rebounding alpha particle? The gold nucleus has a mass of 197 u and the alpha has a mass of 4.0 u.

K1+K2=3.94MeV

## The Attempt at a Solution

Since the alpha particle will momentarily stop when the repulsion between the two particles is enough to stop it, the kinetic energy from the particle will all be converted into potential energy so K1f+K2f=3.94Mev. But I'm not sure where to go from here? I feel like I'm missing something simple

You are missing conservation of momentum.

At the point where the alpha particle stops the gold nucleus is already moving, but details of the collision process are not relevant here.

as mfb hints...you need first to consider conservation of MOMENTUM to find the recoil velocities...the calculate the KEs

## 1. What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision.

## 2. What is an alpha particle?

An alpha particle is a type of particle that consists of two protons and two neutrons, making it essentially a helium nucleus. It is commonly emitted during radioactive decay.

## 3. What is a gold nucleus?

A gold nucleus is the central part of an atom of gold, which is made up of protons and neutrons. It has a positive charge and is surrounded by electrons.

## 4. How does an elastic collision between an alpha particle and gold nucleus occur?

In an elastic collision between an alpha particle and a gold nucleus, the alpha particle approaches the gold nucleus with a certain velocity. When they collide, the alpha particle bounces off the gold nucleus, transferring some of its kinetic energy to the nucleus and causing it to recoil slightly. The total kinetic energy is conserved, and both particles continue moving after the collision.

## 5. What happens to the alpha particle and gold nucleus after an elastic collision?

After an elastic collision, the alpha particle and gold nucleus will continue moving with their respective velocities. However, their velocities and directions may change due to the transfer of kinetic energy during the collision.

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