When `10^(19)` electrons are removed from a neutral metal plate through some process, then the charge on it becomes

Options

A. `+1.6 C`
B. `-1.6 C`
C. `10^(19) C`
D. `10^(-19) C`

Answer

To solve the problem of determining the charge on a neutral metal plate after removing \(10^{19}\) electrons, we can follow these steps:

### Step 1: Understand the initial condition
Initially, the metal plate is neutral, which means it has an equal number of protons and electrons. The charge of the plate is zero.

**Hint:** Remember that a neutral object has equal positive and negative charges.

### Step 2: Determine the effect of removing electrons
When \(10^{19}\) electrons are removed from the plate, the number of protons (which are positively charged) remains the same, while the number of electrons decreases. This results in a net positive charge on the plate.

**Hint:** Removing negatively charged particles (electrons) leads to a positive charge.

### Step 3: Calculate the total charge
The charge of one electron is approximately \( -1.6 \times 10^{-19} \, \text{C} \). Since we are removing electrons, we can calculate the total charge that corresponds to the removal of \(10^{19}\) electrons using the formula:

\[ Q = N \times E \]

Where:
- \(Q\) is the total charge,
- \(N\) is the number of electrons removed (\(10^{19}\)),
- \(E\) is the charge of one electron (\(1.6 \times 10^{-19} \, \text{C}\)).

Substituting the values:

\[ Q = 10^{19} \times (1.6 \times 10^{-19}) \]

### Step 4: Perform the multiplication
Now, we can perform the multiplication:

\[ Q = 10^{19} \times 1.6 \times 10^{-19} = 1.6 \, \text{C} \]

### Step 5: Determine the sign of the charge
Since we removed electrons, the charge on the plate is positive. Therefore, the final charge on the plate is \( +1.6 \, \text{C} \).

**Hint:** The charge is positive because we removed negative charges.

### Final Answer
The charge on the metal plate after removing \(10^{19}\) electrons is \( +1.6 \, \text{C} \).