Chapter 32, Problem 11Q

To determine

Why there is no charge state as $Q=-2$ for $\Delta$ baryon.

Answer to Problem 11Q

Solution:

There is no possibility of charge as $Q=-2$ for $\Delta$ baryon.

Explanation of Solution

The spin of $\Delta$ baryon is $\left(\frac{3}{2}\right)$. This implies that the baryon consists of three quarks and no antiquarks. The charge on the up quark is $\left(+\frac{2}{3}\right)$ and on down quark is $\left(\frac{-1}{3}\right)$.

It is given that the given baryon has charge +2, +1, -1.

The given charges can make only with the following charge combinations.

$\begin{array}{c}Q=+2\\ =\left(\frac{2}{3}+\frac{2}{3}+\frac{2}{3}\right)\\ Q=-1\\ =\left(\frac{-1}{3}+\frac{-1}{3}+\frac{-1}{3}\right)\\ Q=0\\ =\left(\frac{2}{3}+\frac{-1}{3}+\frac{-1}{3}\right)\end{array}$

There is no possibility of charge -2.