Question

The number of electrons that must be removed from a piece of metal to give it a charge of \( 1\times10^{-7} \) coulomb will be:

• A. \( 10^{7} \)
• B. \( 1.6\times10^{19} \)
• C. \( 6.25\times10^{11} \)
• D. \( 9\times10^{12} \)

Hint:

Charge is quantised: use \( n = Q/e \) with \( e = 1.6\times10^{-19} \) C.

Answer 1

The Correct Option is C

Step 1: Use the quantisation of charge.
Charge is quantised, meaning any charge \( Q \) is an integer multiple of the elementary charge \( e \):
\[ Q = n\,e \]
where \( n \) is the number of electrons and \( e = 1.6\times10^{-19}\ \text{C} \).

Step 2: Rearrange for the number of electrons.
\[ n = \frac{Q}{e} \]

Step 3: Substitute the values.
\[ n = \frac{1\times10^{-7}}{1.6\times10^{-19}} \]

Step 4: Do the arithmetic.
\[ n = \frac{1}{1.6}\times10^{-7-(-19)} = 0.625\times10^{12} = 6.25\times10^{11} \]

Step 5: Choose the correct option.
The result matches option (iii). Option (ii) \( 1.6\times10^{19} \) is just the reciprocal of \( e \) and is far too large; options (i) and (iv) do not follow from the calculation.

\[\boxed{n = 6.25\times10^{11}\ \text{electrons}}\]