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The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:
- a)0.877 MeV
- b)0.145 MeV
- c)0.214 MeV
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The kinetic energy of an electron moving with a speed of 0.8c and rest...
According to classical physics, the inertial mass of a body is independent of the velocity of light. It is regarding as a constant. However special theory of relativity leads us to the concept of variation of mass with velocity. It follows from special theory of relativity that the mass m of a body moving with relativistic velocity v relative to an observer is larger than its m0 when it is at rest.
According to Einstein, the mass of the body in motion is different from the mass of the body at rest.
This is the relative formula for variation of mass with velocity where m0 is the rest mass and m is the relativistic mass of the body.
Total energy = Rest energy + Kinetic Energy
Since E = mc2
mc2 = moc2 + KE
K E = (m – mo) c2
This can be written as:
This is the relative formula for variation of mass with velocity where m0 is the rest mass and m is the relativistic mass of the body.
Total energy = Rest energy + Kinetic Energy
Since E = mc2
mc2 = moc2 + KE
K E = (m – mo) c2
This can be written as:
Most Upvoted Answer
The kinetic energy of an electron moving with a speed of 0.8c and rest...
Calculating Kinetic Energy of an Electron:
To calculate the kinetic energy of an electron moving at a relativistic speed, we need to consider the special theory of relativity. The formula to calculate the kinetic energy of a particle moving at a relativistic speed is given by:
KE = (γ - 1) * rest mass energy
Where:
KE = Kinetic Energy
γ = Lorentz factor
Rest mass energy = Energy equivalent of the rest mass of the particle
Calculating Lorentz Factor:
The Lorentz factor (γ) can be calculated using the formula:
γ = 1 / sqrt(1 - v^2/c^2)
Given:
Speed of the electron (v) = 0.8c
Rest mass energy = 0.321 MeV
Substitute the values:
v = 0.8c = 0.8 * speed of light (c)
c = speed of light = 3 x 10^8 m/s
Calculate the Lorentz factor (γ) using the formula above.
Calculate Kinetic Energy:
Once you have calculated the Lorentz factor, substitute it into the first formula to find the kinetic energy of the electron.
KE = (γ - 1) * rest mass energy
Final Answer:
By plugging in the values and solving the equations, you will find the kinetic energy of the electron moving at 0.8c is approximately 0.214 MeV. Therefore, the correct answer is option 'C'.
To calculate the kinetic energy of an electron moving at a relativistic speed, we need to consider the special theory of relativity. The formula to calculate the kinetic energy of a particle moving at a relativistic speed is given by:
KE = (γ - 1) * rest mass energy
Where:
KE = Kinetic Energy
γ = Lorentz factor
Rest mass energy = Energy equivalent of the rest mass of the particle
Calculating Lorentz Factor:
The Lorentz factor (γ) can be calculated using the formula:
γ = 1 / sqrt(1 - v^2/c^2)
Given:
Speed of the electron (v) = 0.8c
Rest mass energy = 0.321 MeV
Substitute the values:
v = 0.8c = 0.8 * speed of light (c)
c = speed of light = 3 x 10^8 m/s
Calculate the Lorentz factor (γ) using the formula above.
Calculate Kinetic Energy:
Once you have calculated the Lorentz factor, substitute it into the first formula to find the kinetic energy of the electron.
KE = (γ - 1) * rest mass energy
Final Answer:
By plugging in the values and solving the equations, you will find the kinetic energy of the electron moving at 0.8c is approximately 0.214 MeV. Therefore, the correct answer is option 'C'.
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The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for EmSAT Achieve 2025 is part of EmSAT Achieve preparation. The Question and answers have been prepared according to the EmSAT Achieve exam syllabus. Information about The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for EmSAT Achieve 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for EmSAT Achieve 2025 is part of EmSAT Achieve preparation. The Question and answers have been prepared according to the EmSAT Achieve exam syllabus. Information about The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for EmSAT Achieve 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The kinetic energy of an electron moving with a speed of 0.8c and rest mass energy of 0.321 MeV is:a)0.877 MeVb)0.145 MeVc)0.214 MeVd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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