A proton is about `1840` times heavier than an electron. When it is accelerated by a potential difference difference of `1kV`, its kinetic enegry will be

Options

A. 1840 keV
B. 1/1840 keV
C. 1 keV
D. 920 keV

Explanation

To find the kinetic energy of a proton when it is accelerated by a potential difference of 1 kV, we can follow these steps:

### Step 1: Understand the relationship between potential difference and kinetic energy
When a charged particle is accelerated through a potential difference (V), the kinetic energy (K.E.) gained by the particle is given by the formula:
\[ K.E. = q \times V \]
where:
- \( q \) is the charge of the particle,
- \( V \) is the potential difference.

### Step 2: Identify the charge of the proton
The charge of a proton is the same as the elementary charge, which is:
\[ q = 1.6 \times 10^{-19} \text{ C} \]

### Step 3: Convert the potential difference to volts
The potential difference given is:
\[ V = 1 \text{ kV} = 1000 \text{ V} \]

### Step 4: Substitute the values into the kinetic energy formula
Now, we can substitute the values of \( q \) and \( V \) into the kinetic energy formula:
\[ K.E. = (1.6 \times 10^{-19} \text{ C}) \times (1000 \text{ V}) \]

### Step 5: Calculate the kinetic energy in joules
Now, performing the multiplication:
\[ K.E. = 1.6 \times 10^{-19} \times 1000 = 1.6 \times 10^{-16} \text{ J} \]

### Step 6: Convert the kinetic energy to electron volts
Since 1 electron volt (eV) is defined as the energy gained by a charge of 1.6 x 10^-19 C when accelerated through a potential difference of 1 V, we can convert joules to electron volts:
\[ K.E. = \frac{1.6 \times 10^{-16} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} = 1000 \text{ eV} \]

### Step 7: Final result in kilo electron volts
Since \( 1000 \text{ eV} = 1 \text{ keV} \), we can express the kinetic energy as:
\[ K.E. = 1 \text{ keV} \]

Thus, the kinetic energy of the proton when it is accelerated by a potential difference of 1 kV is **1 keV**.

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