A Copper atom has 29 electrons revolving around the nucleus. A copper ball contains `4 xx 10^(23)` atoms. What fraction of the electrons be removed to give the ball a charge of `+9.6 mu C`?

Options

A. `~1.8 xx 10^(-13)`
B. `~ 1.3 xx 10^(-12)`
C. `6 xx 10^(-10)`
D. `~ 5.2 xx 10^(-12)`

Answer

To solve the problem step by step, we will follow the logical sequence outlined in the video transcript.

### Step 1: Determine the total number of electrons in the copper ball
Each copper atom has 29 electrons, and the copper ball contains \(4 \times 10^{23}\) atoms.

Total number of electrons in the copper ball can be calculated as:
\[ \text{Total electrons} = \text{Number of atoms} \times \text{Electrons per atom} = 4 \times 10^{23} \times 29 \]

### Step 2: Calculate the total number of electrons
Calculating the total number of electrons:
\[ \text{Total electrons} = 4 \times 10^{23} \times 29 = 1.16 \times 10^{25} \]

### Step 3: Determine the charge of the copper ball
We need to give the copper ball a charge of \(+9.6 \, \mu C\).

### Step 4: Relate charge to the number of electrons removed
The charge \(q\) can be expressed in terms of the number of electrons \(n\) removed:
\[ q = n \times e \]
where \(e\) is the charge of a single electron, approximately \(1.6 \times 10^{-19} \, C\).

### Step 5: Calculate the number of electrons to be removed
Rearranging the formula gives:
\[ n = \frac{q}{e} \]
Substituting the values:
\[ n = \frac{9.6 \times 10^{-6}}{1.6 \times 10^{-19}} = 6 \times 10^{13} \]

### Step 6: Calculate the fraction of electrons removed
The fraction of electrons removed from the total number of electrons is given by:
\[ \text{Fraction} = \frac{n}{\text{Total electrons}} = \frac{6 \times 10^{13}}{1.16 \times 10^{25}} \]

### Step 7: Simplify the fraction
Calculating the fraction:
\[ \text{Fraction} = \frac{6 \times 10^{13}}{1.16 \times 10^{25}} = \frac{6}{1.16} \times 10^{-12} \approx 5.17 \times 10^{-12} \]

### Step 8: Final answer
Thus, the fraction of electrons that need to be removed to give the ball a charge of \(+9.6 \, \mu C\) is approximately:
\[ 5.2 \times 10^{-12} \]