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The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.
Correct answer is '0.67'. Can you explain this answer?
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Introduction:
Cerenkov radiation is the electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The minimum energy required for an electron to emit Cerenkov radiation can be calculated using the Cerenkov threshold equation.
Given data:
Rest mass of the electron (m) = 0.5 MeV
Refractive index of water (n) = 1.5
Calculating the minimum energy:
The Cerenkov threshold equation is given by:
E = m / sqrt(1 - (1/n^2))
Substituting the given values, we have:
E = 0.5 / sqrt(1 - (1/1.5^2))
Simplifying the equation further:
E = 0.5 / sqrt(1 - 1/2.25)
E = 0.5 / sqrt(1 - 0.4444)
E = 0.5 / sqrt(0.5556)
E = 0.5 / 0.7454
E ≈ 0.67 MeV
Therefore, the minimum energy of the electron that can emit Cerenkov radiation while passing through water is approximately 0.67 MeV.
Explanation:
Cerenkov radiation occurs when a charged particle travels through a dielectric medium at a velocity greater than the phase velocity of light in that medium. The refractive index of a medium determines the phase velocity of light in it. In this case, the refractive index of water is given as 1.5.
The Cerenkov threshold equation relates the minimum energy of the particle to its rest mass and the refractive index of the medium. By substituting the given values into the equation and simplifying, we can calculate the minimum energy required for the electron to emit Cerenkov radiation.
In this case, the minimum energy is found to be approximately 0.67 MeV. This means that an electron with an energy greater than or equal to 0.67 MeV can emit Cerenkov radiation while passing through water.
Cerenkov radiation is the electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The minimum energy required for an electron to emit Cerenkov radiation can be calculated using the Cerenkov threshold equation.
Given data:
Rest mass of the electron (m) = 0.5 MeV
Refractive index of water (n) = 1.5
Calculating the minimum energy:
The Cerenkov threshold equation is given by:
E = m / sqrt(1 - (1/n^2))
Substituting the given values, we have:
E = 0.5 / sqrt(1 - (1/1.5^2))
Simplifying the equation further:
E = 0.5 / sqrt(1 - 1/2.25)
E = 0.5 / sqrt(1 - 0.4444)
E = 0.5 / sqrt(0.5556)
E = 0.5 / 0.7454
E ≈ 0.67 MeV
Therefore, the minimum energy of the electron that can emit Cerenkov radiation while passing through water is approximately 0.67 MeV.
Explanation:
Cerenkov radiation occurs when a charged particle travels through a dielectric medium at a velocity greater than the phase velocity of light in that medium. The refractive index of a medium determines the phase velocity of light in it. In this case, the refractive index of water is given as 1.5.
The Cerenkov threshold equation relates the minimum energy of the particle to its rest mass and the refractive index of the medium. By substituting the given values into the equation and simplifying, we can calculate the minimum energy required for the electron to emit Cerenkov radiation.
In this case, the minimum energy is found to be approximately 0.67 MeV. This means that an electron with an energy greater than or equal to 0.67 MeV can emit Cerenkov radiation while passing through water.
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The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.Correct answer is '0.67'. Can you explain this answer?
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The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.Correct answer is '0.67'. 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 The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.Correct answer is '0.67'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.Correct answer is '0.67'. Can you explain this answer?.
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