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Sodium contains 2.54 x1022 free electrons per cm3 ( given = 6.63 x 10 -34 J-s, m= 9 .11 x 10-31 kg , kB = 1.38 x 10-23 JIK and 1eV = 1.6 x 10-19 J ) , then Fermi D 4 temperature is given in terms of 104 K as?
Correct answer is '3.6'. Can you explain this answer?
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Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -3...
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The correct answer is: 3.6
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The correct answer is: 3.6
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Community Answer
Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -3...
Given data:
- Number of free electrons per cm^3 in sodium, n = 2.54 x 10^22 cm^-3
- Planck's constant, h = 6.63 x 10^-34 J-s
- Mass of electron, m = 9.11 x 10^-31 kg
- Boltzmann constant, kB = 1.38 x 10^-23 J/K
- Conversion factor, 1 eV = 1.6 x 10^-19 J
Fermi-Dirac Statistics:
Fermi-Dirac statistics describe the behavior of particles with half-integer spins, such as electrons. According to Fermi-Dirac statistics, the probability of finding a particle with a certain energy is given by the Fermi-Dirac distribution function.
Fermi Energy:
The Fermi energy is the maximum energy of an electron at absolute zero temperature. It is denoted by Ef and is given by the formula:
Ef = (h^2 / 2m) * (3n / 8π)^(2/3)
where h is Planck's constant, m is the mass of the electron, and n is the number of free electrons per unit volume.
Converting cm^-3 to m^-3:
To use the formula for Fermi energy, we need to convert the number of free electrons from cm^-3 to m^-3.
1 cm^-3 = (1 x 10^-2 m)^-3 = 1 x 10^6 m^-3
Therefore, the number of free electrons per m^-3 is:
n = (2.54 x 10^22 cm^-3) x (1 x 10^6 m^-3/cm^-3) = 2.54 x 10^28 m^-3
Calculating Fermi Energy:
Using the given values, we can calculate the Fermi energy as follows:
Ef = (h^2 / 2m) * (3n / 8π)^(2/3)
= ((6.63 x 10^-34 J-s)^2 / (2 x 9.11 x 10^-31 kg)) * (3(2.54 x 10^28 m^-3) / (8π))^(2/3)
= (4.83 x 10^-68 J^2-s^2 / kg) * (1.91 x 10^28 m^-3)^(2/3)
Simplifying the calculation:
Ef = 7.18 x 10^-68 J^2-s^2 / kg * (1.91 x 10^28)^(2/3) m^-2
Converting Fermi Energy to eV:
Since the given answer is in terms of 10^4 K, we need to convert the Fermi energy from joules to electron volts.
1 eV = 1.6 x 10^-19 J
Therefore, the Fermi energy in eV is:
Ef (eV) = Ef / (1.6 x 10^-19 J/eV)
Calculating the Fermi Temperature:
The Fermi temperature (TF) is defined as the temperature at which the thermal energy (
- Number of free electrons per cm^3 in sodium, n = 2.54 x 10^22 cm^-3
- Planck's constant, h = 6.63 x 10^-34 J-s
- Mass of electron, m = 9.11 x 10^-31 kg
- Boltzmann constant, kB = 1.38 x 10^-23 J/K
- Conversion factor, 1 eV = 1.6 x 10^-19 J
Fermi-Dirac Statistics:
Fermi-Dirac statistics describe the behavior of particles with half-integer spins, such as electrons. According to Fermi-Dirac statistics, the probability of finding a particle with a certain energy is given by the Fermi-Dirac distribution function.
Fermi Energy:
The Fermi energy is the maximum energy of an electron at absolute zero temperature. It is denoted by Ef and is given by the formula:
Ef = (h^2 / 2m) * (3n / 8π)^(2/3)
where h is Planck's constant, m is the mass of the electron, and n is the number of free electrons per unit volume.
Converting cm^-3 to m^-3:
To use the formula for Fermi energy, we need to convert the number of free electrons from cm^-3 to m^-3.
1 cm^-3 = (1 x 10^-2 m)^-3 = 1 x 10^6 m^-3
Therefore, the number of free electrons per m^-3 is:
n = (2.54 x 10^22 cm^-3) x (1 x 10^6 m^-3/cm^-3) = 2.54 x 10^28 m^-3
Calculating Fermi Energy:
Using the given values, we can calculate the Fermi energy as follows:
Ef = (h^2 / 2m) * (3n / 8π)^(2/3)
= ((6.63 x 10^-34 J-s)^2 / (2 x 9.11 x 10^-31 kg)) * (3(2.54 x 10^28 m^-3) / (8π))^(2/3)
= (4.83 x 10^-68 J^2-s^2 / kg) * (1.91 x 10^28 m^-3)^(2/3)
Simplifying the calculation:
Ef = 7.18 x 10^-68 J^2-s^2 / kg * (1.91 x 10^28)^(2/3) m^-2
Converting Fermi Energy to eV:
Since the given answer is in terms of 10^4 K, we need to convert the Fermi energy from joules to electron volts.
1 eV = 1.6 x 10^-19 J
Therefore, the Fermi energy in eV is:
Ef (eV) = Ef / (1.6 x 10^-19 J/eV)
Calculating the Fermi Temperature:
The Fermi temperature (TF) is defined as the temperature at which the thermal energy (
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Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer?
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Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer?.
Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sodium contains 2.54 x1022free electrons per cm3( given = 6.63 x 10 -34J-s, m=9 .11 x 10-31kg , kB= 1.38 x 10-23JIK and 1eV = 1.6 x 10-19J ) , then Fermi D 4 temperature is given in terms of 104 K as?Correct answer is '3.6'. Can you explain this answer?.
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