Kinetic energy of an electron accelerated in a potential difference of `100 V` is

Options

A. `1.6 xx 10^(-17) J`
B. `1.6 xx 10^(21) J`
C. `1.6 xx 10^(-29) J`
D. `1.6 xx 10^(-34) J`

Explanation

To find the kinetic energy of an electron accelerated through a potential difference of 100 V, we can use the formula that relates electric potential energy to kinetic energy. Here’s the step-by-step solution:

### Step 1: Understand the relationship between potential difference and kinetic energy
When an electron is accelerated through a potential difference (V), it gains kinetic energy (K.E.) equal to the work done on it by the electric field. The formula to calculate the kinetic energy gained by a charge (q) when it is accelerated through a potential difference (V) is given by:
\[ K.E. = q \cdot V \]

### Step 2: Identify the charge of the electron
The charge of an electron (q) is approximately:
\[ q = 1.6 \times 10^{-19} \, \text{C} \]

### Step 3: Substitute the values into the formula
Now, we substitute the values of the charge and the potential difference into the kinetic energy formula:
\[ K.E. = (1.6 \times 10^{-19} \, \text{C}) \cdot (100 \, \text{V}) \]

### Step 4: Calculate the kinetic energy
Calculating the above expression:
\[ K.E. = 1.6 \times 10^{-19} \times 100 \]
\[ K.E. = 1.6 \times 10^{-17} \, \text{J} \]

### Step 5: State the final answer
Thus, the kinetic energy of the electron accelerated through a potential difference of 100 V is:
\[ K.E. = 1.6 \times 10^{-17} \, \text{J} \]