A body has `-80` micro coulomb of charge. Number of additional electrons in it will be

Options

A. `8 xx 10^(-5)`
B. `80 xx 10^(-17)`
C. `5 xx 10^(14)`
D. `1.28 xx 10^(-17)`

Answer

To find the number of additional electrons in a body with a charge of `-80 micro coulombs`, we can follow these steps:

### Step 1: Understand the Charge of an Electron
The charge of a single electron (e) is approximately `1.6 x 10^(-19) coulombs`.

### Step 2: Convert the Charge from Microcoulombs to Coulombs
The charge of the body is given as `-80 micro coulombs`. We need to convert this to coulombs:
\[ -80 \, \text{micro coulombs} = -80 \times 10^{-6} \, \text{coulombs} = -8.0 \times 10^{-5} \, \text{coulombs} \]

### Step 3: Use the Formula for Quantization of Charge
The total charge (Q) can be expressed in terms of the number of electrons (n) as:
\[ Q = n \times e \]
Where:
- Q is the total charge,
- n is the number of electrons,
- e is the charge of a single electron.

### Step 4: Rearrange the Formula to Solve for n
To find the number of electrons (n), we rearrange the formula:
\[ n = \frac{Q}{e} \]

### Step 5: Substitute the Values into the Formula
Substituting the values we have:
\[ n = \frac{-8.0 \times 10^{-5}}{1.6 \times 10^{-19}} \]

### Step 6: Perform the Calculation
Calculating the above expression:
\[ n = \frac{-8.0}{1.6} \times \frac{10^{-5}}{10^{-19}} = -5 \times 10^{14} \]

### Step 7: Interpret the Result
Since the charge is negative, it indicates that the body has an excess of electrons. Therefore, the number of additional electrons in the body is:
\[ n = 5 \times 10^{14} \]

### Final Answer
The number of additional electrons in the body is \( 5 \times 10^{14} \).

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