Question

(a) What is the strength of the weak nuclear force relative to the strong nuclear force?

(b) What is the strength of the weak nuclear force relative to the electromagnetic force?

Since the weak nuclear force acts at only very short distances, such as inside nuclei, where the strong and electromagnetic forces also act, it might seem surprising that we have any knowledge of it at all. We have such knowledge because the weak nuclear force is responsible for beta decay, a type of nuclear decay not explained by other forces.

Short answer

(a) The strength of weak nuclear force relative to strong nuclear force is${10}^{-13}$.

(b) The strength of weak nuclear force relative to electromagnetic force is ${10}^{-11}$.

Step-by-step solution

(a) Strength of weak nuclear force relative to the strong nuclear force

Nuclear forces play a vital role in the structure of matter, and they act over a short-range. These forces help in determining the stability of nuclei.

The relative strength of the weak nuclear force is of the order of${10}^{-13}$whereas the relative strength of the strong nuclear force is 1.

Determine the ratio of the weak nuclear force to the strong nuclear force as:

$$\begin{gathered} \frac{F_{N,w}}{F_{N,s}}=\frac{{10}^{-13}}{1} \\ ={10}^{-13} \end{gathered}$$

Here$F_{N,w}$ is the weak nuclear force, and$F_{N,s}$ is the strong nuclear force.

Hence, the strength of weak nuclear force relative to strong nuclear force is ${10}^{-13}$.

(b) Strength of weak nuclear force relative to the electromagnetic force

Electromagnetic forces are long-range forces that act over large distances. These forces can be attractive or repulsive in nature.

The relative strength of the electromagnetic force is${10}^{-2}$.

Determine the ratio of the weak nuclear force to the electromagnetic force as:

$$\begin{gathered} \frac{F_{N,w}}{F_{electric}}=\frac{{10}^{-13}}{{10}^{-2}} \\ ={10}^{-11} \end{gathered}$$

Here$F_{electric}$ is the electromagnetic force.

Hence, the strength of weak nuclear force relative to electromagnetic force is ${10}^{-11}$.