6. The kinetic energy of an electron is 55% of its rest mass energy. Find the speed of the electron. с

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**Problem 6:**

The kinetic energy of an electron is 55% of its rest mass energy. Find the speed of the electron.

**Explanation:**

- This problem involves finding the speed of an electron given that its kinetic energy is a specific percentage of its rest mass energy.
- To solve this type of problem, you would typically use the theory of relativity. The rest mass energy of an electron is given by \( E_0 = m_0c^2 \), where \( m_0 \) is the rest mass of the electron and \( c \) is the speed of light. 
- The given information states that the kinetic energy \( K \) is 55% of the rest mass energy, \( K = 0.55E_0 \). 
- You can relate kinetic energy and speed using the relativistic energy-momentum relationship:

\[ E = \gamma m_0c^2 \]

where \( \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} \) is the Lorentz factor.

- Solving for the speed \( v \) involves substituting \( K = E - m_0c^2 \) into the equations and solving for \( v \).
Transcribed Image Text:**Problem 6:** The kinetic energy of an electron is 55% of its rest mass energy. Find the speed of the electron. **Explanation:** - This problem involves finding the speed of an electron given that its kinetic energy is a specific percentage of its rest mass energy. - To solve this type of problem, you would typically use the theory of relativity. The rest mass energy of an electron is given by \( E_0 = m_0c^2 \), where \( m_0 \) is the rest mass of the electron and \( c \) is the speed of light. - The given information states that the kinetic energy \( K \) is 55% of the rest mass energy, \( K = 0.55E_0 \). - You can relate kinetic energy and speed using the relativistic energy-momentum relationship: \[ E = \gamma m_0c^2 \] where \( \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} \) is the Lorentz factor. - Solving for the speed \( v \) involves substituting \( K = E - m_0c^2 \) into the equations and solving for \( v \).
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