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^(-19)` J
C. `1.6 xx 10^(-21)` J
D. `1.6 xx 10^(-25)`J

Answer

To find the kinetic energy of an electron accelerated in a potential difference of 100 V, we can follow these steps:

### Step 1: Understand the relationship between voltage and work done
The voltage (V) is defined as the work done (W) per unit charge (Q). Mathematically, this can be expressed as:
\[ V = \frac{W}{Q} \]
From this, we can rearrange the formula to find the work done:
\[ W = V \times Q \]

### Step 2: Identify the values
In this problem, we are given:
- Voltage (V) = 100 V
- Charge of an electron (Q) = \( 1.6 \times 10^{-19} \) Coulombs

### Step 3: Substitute the values into the equation
Now we can substitute the known values into the equation for work done:
\[ W = 100 \, \text{V} \times 1.6 \times 10^{-19} \, \text{C} \]

### Step 4: Calculate the work done
Now, we perform the multiplication:
\[ W = 100 \times 1.6 \times 10^{-19} = 1.6 \times 10^{-17} \, \text{J} \]

### Step 5: Relate work done to kinetic energy
The work done on the electron is converted into kinetic energy (KE) as it is accelerated through the potential difference. Therefore, the kinetic energy of the electron is:
\[ KE = W = 1.6 \times 10^{-17} \, \text{J} \]

### Final Answer
The kinetic energy of an electron accelerated in a potential difference of 100 V is:
\[ KE = 1.6 \times 10^{-17} \, \text{J} \]

---