Particle Physics: Question 6

Worked solution

Step 1: List the individual quark charges

The baryon is made of one up quark, one down quark and one strange quark. Using the given charges: $\text{up} = +\frac23e, \quad \text{down} = -\frac13e, \quad \text{strange} = -\frac13e$

Step 2: Sum the three charges

$Q = \left(+\frac23e\right) + \left(-\frac13e\right) + \left(-\frac13e\right)$

Combining the two negative terms first: $-\frac13e - \frac13e = -\frac23e$

Then adding the up quark’s contribution: $Q = +\frac23e - \frac23e = 0$

Step 3: Why the other options are wrong

• Option A ($-1e$) would result from treating all three quarks as carrying charge $-\frac13e$, ignoring that the up quark is positive.
• Option B ($-\frac13e$) would result from adding only the down and strange quark charges and forgetting the up quark’s contribution entirely.
• Option D ($+\frac23e$) would result from adding only the up and one of the negative charges but forgetting the second $-\frac13e$ contribution (e.g. from the strange quark).

Final answer

• The total charge of the $uds$ baryon is $\boxed{0}$, option C. (This combination corresponds to the real particle known as the $\Lambda^0$ baryon.)