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The density of states for electron hi a metal is given by D (E)dE = 13.6x 1027 E1/2 dE and ρ = 8.5 x 1028 /m3. The energy of Fermi level is___________eV. (Round off to three decimal places)
Correct answer is between '4.443,4.446'. Can you explain this answer?
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The density of states for electron hi a metal is given by D(E)dE = 13....
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The density of states for electron hi a metal is given by D(E)dE = 13....
The energy E is measured in electron volts (eV).
To find the total number of states in the energy range from E1 to E2, we need to integrate the density of states over that range.
The density of states is given by D(E)dE = 13.6x 10^27 E^(1/2) dE.
To integrate this expression, we first rewrite it as D(E) = 13.6x 10^27 E^(1/2).
Now we can integrate D(E) from E1 to E2:
∫D(E) dE = ∫13.6x 10^27 E^(1/2) dE
Using the power rule of integration, we can simplify the expression:
∫D(E) dE = 13.6x 10^27 ∫E^(1/2) dE
= 13.6x 10^27 * (2/3) E^(3/2) + C
where C is the constant of integration.
Now we can evaluate the integral at the limits E1 and E2:
∫D(E) dE = (2/3) * 13.6x 10^27 * (E2^(3/2) - E1^(3/2))
So, the total number of states in the energy range from E1 to E2 is given by:
N = (2/3) * 13.6x 10^27 * (E2^(3/2) - E1^(3/2))
To find the total number of states in the energy range from E1 to E2, we need to integrate the density of states over that range.
The density of states is given by D(E)dE = 13.6x 10^27 E^(1/2) dE.
To integrate this expression, we first rewrite it as D(E) = 13.6x 10^27 E^(1/2).
Now we can integrate D(E) from E1 to E2:
∫D(E) dE = ∫13.6x 10^27 E^(1/2) dE
Using the power rule of integration, we can simplify the expression:
∫D(E) dE = 13.6x 10^27 ∫E^(1/2) dE
= 13.6x 10^27 * (2/3) E^(3/2) + C
where C is the constant of integration.
Now we can evaluate the integral at the limits E1 and E2:
∫D(E) dE = (2/3) * 13.6x 10^27 * (E2^(3/2) - E1^(3/2))
So, the total number of states in the energy range from E1 to E2 is given by:
N = (2/3) * 13.6x 10^27 * (E2^(3/2) - E1^(3/2))
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The density of states for electron hi a metal is given by D(E)dE = 13.6x 1027 E1/2 dE and ρ = 8.5 x 1028/m3. The energy of Fermi level is___________eV. (Round off to three decimal places)Correct answer is between '4.443,4.446'. Can you explain this answer?
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The density of states for electron hi a metal is given by D(E)dE = 13.6x 1027 E1/2 dE and ρ = 8.5 x 1028/m3. The energy of Fermi level is___________eV. (Round off to three decimal places)Correct answer is between '4.443,4.446'. 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 density of states for electron hi a metal is given by D(E)dE = 13.6x 1027 E1/2 dE and ρ = 8.5 x 1028/m3. The energy of Fermi level is___________eV. (Round off to three decimal places)Correct answer is between '4.443,4.446'. 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 density of states for electron hi a metal is given by D(E)dE = 13.6x 1027 E1/2 dE and ρ = 8.5 x 1028/m3. The energy of Fermi level is___________eV. (Round off to three decimal places)Correct answer is between '4.443,4.446'. Can you explain this answer?.
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