Chapter 31, Problem 1RQ

To determine

Relationship between the mass for the given kinetic energy and the energy loss rate.

Answer to Problem 1RQ

The energy loss rate is proportional to the mass of the ion.

Explanation of Solution

Write the expression for the energy loss rate.

  $\Delta K\alpha \frac{-m{q}^2}{2K}$        (I)

Here, $\Delta K$ is the energy loss rate, $m$ is the mass of the ion, $q$ is the charge of the ion and $K$ is the kinetic energy of the ion.

Since the energy loss rate is directly proportional to the mass and charge of the ion then it is inversely proportional to the given kinetic energy of the ion. The negative sign in equation (I) indicates the losing of kinetic energy in the ion.

Conclusion:

Therefore, the energy loss rate is proportional to the mass of the ion.