Mass of the proton is 1840 times that of electron. It is accelerated through a potential difference of 1 V. Find its kinetic energy.

Options

A. 1 eV
B. 1 keV
C. 1840 eV
D. 1849 keV

Answer

To find the kinetic energy of a proton that is accelerated through a potential difference of 1 volt, we can follow these steps:

### Step 1: Understand the relationship between charge, potential difference, and kinetic energy.
The kinetic energy (KE) gained by a charged particle when it is accelerated through a potential difference (V) is given by the formula:
\[ KE = Q \cdot V \]
where \( KE \) is the kinetic energy, \( Q \) is the charge of the particle, and \( V \) is the potential difference.

### Step 2: Identify the charge of the proton.
The charge of a proton is equal to the elementary charge, which is approximately:
\[ Q = e = 1.602 \times 10^{-19} \text{ Coulombs} \]

### Step 3: Substitute the values into the kinetic energy formula.
Given that the potential difference \( V \) is 1 volt, we can substitute the values into the formula:
\[ KE = e \cdot V = e \cdot 1 \text{ V} \]
This simplifies to:
\[ KE = e \]

### Step 4: Convert the kinetic energy into electron volts.
Since the charge \( e \) is defined as 1 electron volt (eV) when it is accelerated through a potential difference of 1 volt, we can conclude:
\[ KE = 1 \text{ eV} \]

### Final Answer:
The kinetic energy of the proton when it is accelerated through a potential difference of 1 volt is:
\[ \text{Kinetic Energy} = 1 \text{ eV} \]