The kinetic energy of an electron accelerated from rest through a potential difference of 12V will be:

Options

A. 12V
B. 12eV
C. 12erg
D. 6V

Explanation

To find the kinetic energy of an electron that has been accelerated from rest through a potential difference of 12 volts, we can use the following steps:

### 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 (KE) equal to the work done on it by the electric field. The formula for the kinetic energy gained by a charge (in this case, an electron) when accelerated through a potential difference is given by:

\[ KE = qV \]

where:
- \( KE \) is the kinetic energy,
- \( q \) is the charge of the electron,
- \( V \) is the potential difference.

### 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
Given that the potential difference (\( V \)) is 12 volts, we can substitute the values into the kinetic energy formula:

\[ KE = (1.6 \times 10^{-19} \, \text{C}) \times (12 \, \text{V}) \]

### Step 4: Calculate the kinetic energy
Now, we can perform the multiplication:

\[ KE = 1.6 \times 10^{-19} \times 12 = 1.92 \times 10^{-18} \, \text{J} \]

### Step 5: Convert the kinetic energy to electron volts
Since 1 electron volt (eV) is defined as the energy gained by an electron when it is accelerated through a potential difference of 1 volt, we can express the kinetic energy in electron volts directly:

\[ KE = 12 \, \text{eV} \]

Thus, the kinetic energy of the electron accelerated through a potential difference of 12 volts is **12 eV**.

### Final Answer:
The kinetic energy of the electron is **12 eV**.

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