Question:
An electron is accelerated through a potential difference of 200 V. If \( e/m \) for the electron is \( 1.6 \times 10^{11} \, \text{C/kg} \), the velocity acquired by the electron will be:
An electron is accelerated through a potential difference of 200 V. If \( e/m \) for the electron is \( 1.6 \times 10^{11} \, \text{C/kg} \), the velocity acquired by the electron will be:
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To find the velocity of an accelerated electron, use the formula \( v = \sqrt{\frac{2eV}{m}} \), where \( e \) is the charge, \( V \) is the potential difference, and \( m \) is the electron's mass.
Updated On: Apr 22, 2026
- \( 8 \times 10^6 \) m/s
- \( 8 \times 10^5 \) m/s
- \( 5.9 \times 10^6 \) m/s
- \( 5.9 \times 10^5 \) m/s
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The Correct Option is A
Solution and Explanation
Step 1: Use the kinetic energy formula for an accelerated electron.
The kinetic energy gained by the electron when it is accelerated through a potential difference \( V \) is given by: \[ KE = eV \] where \( e \) is the charge of the electron and \( V = 200 \, \text{V} \).
Step 2: Calculate the velocity.
The kinetic energy is also related to the velocity by: \[ KE = \frac{1}{2} m v^2 \] Equating the two expressions for \( KE \): \[ eV = \frac{1}{2} m v^2 \] Substituting \( e/m = 1.6 \times 10^{11} \, \text{C/kg} \), we can solve for \( v \): \[ v = \sqrt{\frac{2eV}{m}} = \sqrt{2 \times 1.6 \times 10^{11} \times 200} = 8 \times 10^6 \, \text{m/s} \]
Step 3: Conclusion.
The velocity acquired by the electron is \( 8 \times 10^6 \, \text{m/s} \), which is option (1).
The kinetic energy gained by the electron when it is accelerated through a potential difference \( V \) is given by: \[ KE = eV \] where \( e \) is the charge of the electron and \( V = 200 \, \text{V} \).
Step 2: Calculate the velocity.
The kinetic energy is also related to the velocity by: \[ KE = \frac{1}{2} m v^2 \] Equating the two expressions for \( KE \): \[ eV = \frac{1}{2} m v^2 \] Substituting \( e/m = 1.6 \times 10^{11} \, \text{C/kg} \), we can solve for \( v \): \[ v = \sqrt{\frac{2eV}{m}} = \sqrt{2 \times 1.6 \times 10^{11} \times 200} = 8 \times 10^6 \, \text{m/s} \]
Step 3: Conclusion.
The velocity acquired by the electron is \( 8 \times 10^6 \, \text{m/s} \), which is option (1).
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