How much kinetic energy will be gained by an `alpha-`particle in going from a point at `70 V` to another point at `50 V`

Options

A. 40 eV
B. 40 keV
C. 40 MeV
D. 0 eV

Answer

To find the kinetic energy gained by an alpha particle when it moves from a point at 70 V to another point at 50 V, we can follow these steps:

### Step 1: Understand the concept of electric potential and kinetic energy
The kinetic energy gained by a charged particle moving through an electric potential difference can be calculated using the formula:
\[ K.E. = q \cdot \Delta V \]
where:
- \( K.E. \) is the kinetic energy,
- \( q \) is the charge of the particle,
- \( \Delta V \) is the change in electric potential.

### Step 2: Identify the charge of the alpha particle
An alpha particle consists of 2 protons and 2 neutrons. Therefore, its charge \( q \) is:
\[ q = 2e \]
where \( e \) (the elementary charge) is approximately \( 1.6 \times 10^{-19} \, \text{C} \). Thus,
\[ q = 2 \times 1.6 \times 10^{-19} \, \text{C} = 3.2 \times 10^{-19} \, \text{C} \]

### Step 3: Calculate the change in electric potential
The change in electric potential \( \Delta V \) as the alpha particle moves from 70 V to 50 V is:
\[ \Delta V = V_{\text{final}} - V_{\text{initial}} = 50 \, \text{V} - 70 \, \text{V} = -20 \, \text{V} \]

### Step 4: Substitute values into the kinetic energy formula
Now, we can substitute the values into the kinetic energy formula:
\[ K.E. = q \cdot \Delta V = (2e) \cdot (70 \, \text{V} - 50 \, \text{V}) \]
\[ K.E. = (2 \times 1.6 \times 10^{-19} \, \text{C}) \cdot (20 \, \text{V}) \]

### Step 5: Calculate the kinetic energy
Calculating this gives:
\[ K.E. = 3.2 \times 10^{-19} \, \text{C} \cdot 20 \, \text{V} = 6.4 \times 10^{-18} \, \text{J} \]

### Step 6: Convert to electron volts
Since the question asks for the answer in electron volts (eV), we can convert joules to electron volts using the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ K.E. = \frac{6.4 \times 10^{-18} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} = 40 \, \text{eV} \]

### Final Answer
The kinetic energy gained by the alpha particle is:
\[ K.E. = 40 \, \text{eV} \]

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