Question

If the protons and electrons are the only basic charges in the universe, all the observable charges have to be integral multiples of e. Thus, if an object contains x electrons and y protons, the net charge on the object will be

• A. -(x + y) e
• B. (x + y) e
• C. (x - y) e
• D. (y - x) e

Hint:

Remember that charge is quantized and additive. Always assign a negative sign to the charge of electrons and a positive sign to the charge of protons before summing them up to find the net charge.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The net charge on an object is the algebraic sum of the charges of all its constituent particles. The charge of a single electron is -e, and the charge of a single proton is +e.

Step 3: Detailed Explanation:
An object contains 'x' electrons and 'y' protons.
The total charge due to 'x' electrons = \( x \times (\text{charge of one electron}) = x \times (-e) = -xe \).
The total charge due to 'y' protons = \( y \times (\text{charge of one proton}) = y \times (+e) = +ye \).
The net charge on the object is the sum of these charges:
\[ \text{Net Charge} = (\text{Total charge of electrons}) + (\text{Total charge of protons}) \] \[ \text{Net Charge} = -xe + ye \] Factoring out 'e', we get:
\[ \text{Net Charge} = (y - x)e \]

Step 4: Final Answer:
The net charge on the object will be (y - x)e.