An alpha particle is accelerated from rest through a potential difference of 100 volt. Its final kinetic energy is

Options

A. 100 eV
B. 1000 eV
C. 200 eV
D. 400 eV

Answer

To find the final kinetic energy of an alpha particle accelerated through a potential difference of 100 volts, we can follow these steps:

### Step 1: Understand the relationship between work done and kinetic energy
According to the work-energy theorem, the work done on the particle is equal to the change in kinetic energy. Since the alpha particle starts from rest, its initial kinetic energy is zero. Therefore, the final kinetic energy (KE) is equal to the work done on it.

### Step 2: Calculate the work done on the alpha particle
The work done (W) on a charged particle when it is accelerated through a potential difference (V) is given by the formula:
\[ W = Q \times V \]
where:
- \( Q \) is the charge of the particle,
- \( V \) is the potential difference.

### Step 3: Determine the charge of the alpha particle
An alpha particle consists of 2 protons and 2 neutrons. The charge of a proton is approximately \( e = 1.6 \times 10^{-19} \) coulombs. Therefore, the charge of the alpha particle (Q) is:
\[ Q = 2e = 2 \times 1.6 \times 10^{-19} \, \text{C} = 3.2 \times 10^{-19} \, \text{C} \]

### Step 4: Substitute the values into the work done formula
Given that the potential difference \( V = 100 \, \text{V} \), we can substitute the values into the work done formula:
\[ W = Q \times V = (3.2 \times 10^{-19} \, \text{C}) \times (100 \, \text{V}) \]
\[ W = 3.2 \times 10^{-17} \, \text{J} \]

### Step 5: Convert the work done into electron volts
Since 1 electron volt (eV) is defined as the energy gained by a charge of 1 elementary charge (e) when accelerated through a potential difference of 1 volt, we can convert joules to electron volts:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
To convert the work done from joules to electron volts:
\[ W = \frac{3.2 \times 10^{-17} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} = 200 \, \text{eV} \]

### Step 6: Conclusion
The final kinetic energy of the alpha particle after being accelerated through a potential difference of 100 volts is:
\[ KE = 200 \, \text{eV} \]

Thus, the answer is **200 electron volts**.

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