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Rest mass energy of an electron is 0.51 MeV. A moving electron has a kinetic energy of 9.69 MeV. The ratio of the mass of the moving electron to its rest mass is
- a)1 9 : 1
- b)20:1
- c)1 : 1 9
- d)1 : 2 0
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Rest mass energy of an electron is 0.51 MeV. A moving electron has a k...
E = mc2 - m0c2 ⇒ E = 
9.69 =
10.2 =
m =
9.69 =
10.2 =
m =
Most Upvoted Answer
Rest mass energy of an electron is 0.51 MeV. A moving electron has a k...
Explanation:
Rest mass energy of an electron:
The rest mass energy of an electron is 0.51 MeV. It is the energy equivalent of the rest mass of an electron.
Kinetic energy of an electron:
The kinetic energy of an electron is 9.69 MeV. It is the energy possessed by an electron due to its motion.
Ratio of the mass of the moving electron to its rest mass:
We know that the total energy of a moving electron is the sum of its rest mass energy and kinetic energy.
Total energy (E) = Rest mass energy (E0) + Kinetic energy (K)
E = E0 + K
9.69 MeV = 0.51 MeV + K
K = 9.18 MeV
We also know that the total energy of a moving electron is given by Einstein's famous equation:
E = mc^2
where m is the relativistic mass of the electron, c is the speed of light in vacuum.
So, the relativistic mass of the electron can be calculated as:
m = E/c^2
Substituting the values of energy and speed of light, we get:
m = 9.18 MeV / (3 x 10^8 m/s)^2
m = 1.02 x 10^-30 kg
The ratio of the mass of the moving electron to its rest mass can be calculated as:
Mass ratio = relativistic mass / rest mass
Mass ratio = 1.02 x 10^-30 kg / (9.11 x 10^-31 kg)
Mass ratio = 11.2
Therefore, the correct option is B) 20:1, which is the closest to the calculated mass ratio.
Rest mass energy of an electron:
The rest mass energy of an electron is 0.51 MeV. It is the energy equivalent of the rest mass of an electron.
Kinetic energy of an electron:
The kinetic energy of an electron is 9.69 MeV. It is the energy possessed by an electron due to its motion.
Ratio of the mass of the moving electron to its rest mass:
We know that the total energy of a moving electron is the sum of its rest mass energy and kinetic energy.
Total energy (E) = Rest mass energy (E0) + Kinetic energy (K)
E = E0 + K
9.69 MeV = 0.51 MeV + K
K = 9.18 MeV
We also know that the total energy of a moving electron is given by Einstein's famous equation:
E = mc^2
where m is the relativistic mass of the electron, c is the speed of light in vacuum.
So, the relativistic mass of the electron can be calculated as:
m = E/c^2
Substituting the values of energy and speed of light, we get:
m = 9.18 MeV / (3 x 10^8 m/s)^2
m = 1.02 x 10^-30 kg
The ratio of the mass of the moving electron to its rest mass can be calculated as:
Mass ratio = relativistic mass / rest mass
Mass ratio = 1.02 x 10^-30 kg / (9.11 x 10^-31 kg)
Mass ratio = 11.2
Therefore, the correct option is B) 20:1, which is the closest to the calculated mass ratio.
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Rest mass energy of an electron is 0.51 MeV. A moving electron has a kinetic energy of 9.69 MeV. The ratio of the mass of the moving electron to its restmass isa)1 9 : 1b)20:1c)1 : 1 9d)1 : 2 0Correct answer is option 'B'. Can you explain this answer?
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Rest mass energy of an electron is 0.51 MeV. A moving electron has a kinetic energy of 9.69 MeV. The ratio of the mass of the moving electron to its restmass isa)1 9 : 1b)20:1c)1 : 1 9d)1 : 2 0Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Rest mass energy of an electron is 0.51 MeV. A moving electron has a kinetic energy of 9.69 MeV. The ratio of the mass of the moving electron to its restmass isa)1 9 : 1b)20:1c)1 : 1 9d)1 : 2 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rest mass energy of an electron is 0.51 MeV. A moving electron has a kinetic energy of 9.69 MeV. The ratio of the mass of the moving electron to its restmass isa)1 9 : 1b)20:1c)1 : 1 9d)1 : 2 0Correct answer is option 'B'. Can you explain this answer?.
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