**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 \( v \).

Kinetic energy of an electron is ; here represents rest mass energy of electron.Find:Speed of electron in units of speed of light.Energy possessed by a body due to its motion is known as kinetic energy. When a particle or object moves at a speed comparable to speed of light then it follows relativistic mechanics. The relativistic kinetic energy in terms of rest mass energy is given asHere represents relativistic kinetic energy, represents rest mass energy and represents relativistic factor.Insert the value of kinetic energy into the equation above.The relativistic factor provides the information about change in total energy with velocity or change in total energy of a moving particle with respect to its rest mass energy. It is given asHere represents speed of particle and represents speed of light.Insert the value of relativistic factor into the equation above.Speed of electron is

Answered: 6. The kinetic energy of an electron is…

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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

**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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