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Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2 + constant. The cyclotron resonane for electrons in a field B = 0.1 Weber/m2 occurs at an angular frequency ωe = 1.8 x 1011 rad s-1The value of a is_______x 10-38(in the untis of Jm2)
Correct answer is between '6.1,6.4'. Can you explain this answer?
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Assume that the E vs k relationship for electrons in the conduction ba...
Electron in conduction band behaves as if it had an effective mass m* given by
Cyclotron resonance frequency for the electron is
⇒
Cyclotron resonance frequency for the electron is
⇒
Most Upvoted Answer
Assume that the E vs k relationship for electrons in the conduction ba...
To find the angular frequency of the cyclotron resonance, we need to use the equation:
ω = eB/m*
where ω is the angular frequency, e is the charge of an electron, B is the magnetic field, and m* is the effective mass of the electron.
Given that B = 0.1 Weber/m^2, we can substitute this value into the equation:
ω = (1.6 x 10^-19 C)(0.1 Weber/m^2)/m*
To find the effective mass, we need to use the given E vs k relationship:
E = ak^2
The effective mass can be calculated using the equation:
m* = ħ^2/(d^2E/dk^2)
where ħ is the reduced Planck's constant and d^2E/dk^2 is the second derivative of E with respect to k.
Since the E vs k relationship is given as E = ak^2, the second derivative can be calculated as:
d^2E/dk^2 = 2a
Substituting this value into the equation for the effective mass:
m* = ħ^2/(2a)
Now, we can substitute this value for m* into the equation for ω:
ω = (1.6 x 10^-19 C)(0.1 Weber/m^2) / (ħ^2/(2a))
Simplifying, we get:
ω = 3.2 x 10^18 a (rad/s)
Therefore, the angular frequency of the cyclotron resonance is 3.2 x 10^18 a rad/s, where a is the constant in the E vs k relationship.
ω = eB/m*
where ω is the angular frequency, e is the charge of an electron, B is the magnetic field, and m* is the effective mass of the electron.
Given that B = 0.1 Weber/m^2, we can substitute this value into the equation:
ω = (1.6 x 10^-19 C)(0.1 Weber/m^2)/m*
To find the effective mass, we need to use the given E vs k relationship:
E = ak^2
The effective mass can be calculated using the equation:
m* = ħ^2/(d^2E/dk^2)
where ħ is the reduced Planck's constant and d^2E/dk^2 is the second derivative of E with respect to k.
Since the E vs k relationship is given as E = ak^2, the second derivative can be calculated as:
d^2E/dk^2 = 2a
Substituting this value into the equation for the effective mass:
m* = ħ^2/(2a)
Now, we can substitute this value for m* into the equation for ω:
ω = (1.6 x 10^-19 C)(0.1 Weber/m^2) / (ħ^2/(2a))
Simplifying, we get:
ω = 3.2 x 10^18 a (rad/s)
Therefore, the angular frequency of the cyclotron resonance is 3.2 x 10^18 a rad/s, where a is the constant in the E vs k relationship.
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Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. Can you explain this answer?
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Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. 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 Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. Can you explain this answer?.
Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. 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 Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent n-type semiconductor can be approximated by E = ak2+ constant.The cyclotron resonane for electrons in a field B= 0.1 Weber/m2 occurs at an angular frequencyωe = 1.8 x 1011rad s-1The value of a is_______x 10-38(in the untis of Jm2)Correct answer is between '6.1,6.4'. Can you explain this answer?.
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