Question

about 13.9 the mass of the neutron. What fraction of the neutron’s kinetic energy is transferred to the atomic nucleus? 017 (part 2 of 2) 10.0 points If the initial kinetic energy of the neutron is 1.32 × 10−13 J, find its final kinetic energy. Answer in units of J.

Answer 1

Assuming 13.9% of the neutron's kinetic energy transfers to the atomic nucleus, the final kinetic energy is approximately
`\(1.13692 * 10^(-13)\)`, calculated using the given values and the expression for kinetic energy transfer.

Given that the mass of the neutron is denoted as \(m\) and the mass of the atomic nucleus is 13.9m, the fraction of kinetic energy transferred f is given by:

`\[ f = \frac{\text{kinetic energy transferred}}{\text{initial kinetic energy}} \]`

The final kinetic energy
`(\(K_f\))` can be expressed as:

`\[ K_f = K_i - f \cdot K_i \]`

Now, substitute the values provided:

`\[ K_i = 1.32 * 10^(-13) \, \text{J} \]`

Assuming f is a fraction, you can choose a reasonable value for f (e.g., f = 0.139 for 13.9% transfer) and plug in the values to find
`\(K_f\)`:

`\[ K_f = (1 - 0.139) \cdot 1.32 * 10^(-13) \, \text{J} \]`

`\[ K_f = 0.861 \cdot 1.32 * 10^(-13) \, \text{J} \]`

`\[ K_f \approx 1.13692 * 10^(-13) \, \text{J} \]`

So, if we assume that approximately 13.9% of the neutron's kinetic energy is transferred to the atomic nucleus, the final kinetic energy of the neutron is approximately
`\(1.13692 * 10^(-13)\)` joules.

Complete question:

About 13.9 the mass of the neutron. What fraction of the neutron’s kinetic energy is transferred to the atomic nucleus? If the initial kinetic energy of the neutron is 1.32 × 10−13 J, find its final kinetic energy. Answer in units of J.