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Chapter 11: Problem 40

Based on the quark composition of a neutron, show that is charge is 0 .

Short Answer

Expert verified
The neutron consists of one up quark with charge \(+\frac{2}{3}\) and two down quarks each with charge \(-\frac{1}{3}\). The overall charge of a neutron is calculated by summing the charges of its constituent quarks: \(+\frac{2}{3} -\frac{1}{3} -\frac{1}{3}\) = \(\frac{2 - 1 - 1}{3}\) = \(\frac{0}{3}\). Thus, the charge of a neutron is 0, confirming its neutrality.

Step by step solution

01

1. Determine the charge of quarks present in neutron

The neutron has one up quark and two down quarks. The up quark has a charge of \(+\frac{2}{3}\), and each down quark has a charge of \(-\frac{1}{3}\).
02

2. Calculate the overall charge of the neutron

Now, we need to find the overall charge of the neutron by summing the charges of its constituent quarks: Neutron Charge = (Charge of up quark) + (Charge of 1st down quark) + (Charge of 2nd down quark)
03

3. Substitute the charges of quarks and evaluate the sum

Replace the charges of the quarks in the equation: Neutron Charge = \(+\frac{2}{3} -\frac{1}{3} -\frac{1}{3}\) Now, perform the calculation: Neutron Charge = \(\frac{2}{3} -\frac{1}{3} -\frac{1}{3}\) = \(\frac{2 - 1 - 1}{3}\) = \(\frac{0}{3}\)
04

4. Conclude the result

The overall charge of the neutron is 0, as shown by the quark composition and the calculation. This demonstrates that a neutron is a neutral particle in terms of its electric charge.

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