Question

A proton (mass 1 u) is shot toward an unknown target nucleus at a speed of $2.50\times {10}^6$ m/s. The proton rebounds with its speed reduced by 25% while the target nucleus acquires a speed of $3.12\times {10}^5$ m/s. What is the mass, in atomic mass units, of the target nucleus?

Short answer

Mass of the target nucleus is 14.02u

Step-by-step solution

Step 1. Given information is :Mass of the proton = 1uSpeed of the proton = 2.50×106m/sSpeed acquired by Target Nucleus = 3.12×105m/s

We need to find out the mass of the target nucleus in atomic mass units.

Step 2. Applying Law of conservation of Momentum

As the Proton rebounds with some speed, We can assume the collision to be elastic.

Using Law of conservation of Momentum,

$$\begin{gathered} m_p{v}_{pi}+m_n{v}_{ni}=m_p{v}_{pf}+m_n{v}_{nf} \\ u.2.5\times {10}^{6}m/s+0=\left(u\right)(-0.75\times 2.5\times {10}^{6}m/s)+m_n(3.12\times {10}^{5}m/s) \\ {m}_n=\frac{1.75\times 2.5\times {10}^{6}m/s}{3.12\times {10}^{5}m/s}u \\ {m}_n=14.02u \end{gathered}$$