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`

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 work done and kinetic energy
When an electron is accelerated through a potential difference (V), the work done (W) on the electron is converted into its kinetic energy (KE). This can be expressed as:
\[ KE = W \]

### Step 2: Use the formula for work done
The work done on a charge (Q) when it moves through a potential difference (V) is given by:
\[ W = QV \]
For an electron, the charge (Q) is equal to the elementary charge (e), which is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

### Step 3: Substitute the values into the formula
In this case, the potential difference (V) is given as 100 V. Therefore, the work done on the electron can be calculated as:
\[ W = e \cdot V = (1.6 \times 10^{-19} \, \text{C}) \cdot (100 \, \text{V}) \]

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

### Step 5: Conclude with the kinetic energy
Since the work done is equal to the kinetic energy gained by the electron, we have:
\[ KE = 1.6 \times 10^{-17} \, \text{J} \]

Thus, the kinetic energy of the electron accelerated in a potential difference of 100 V is:
\[ \text{Kinetic Energy} = 1.6 \times 10^{-17} \, \text{J} \]