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An intrinsic semiconducting sample has an energy gap of 0.38eV, calculate the probability at 1000C that the lowest level in the conduction band will be occupied.
- a)3.01 x 10-4
- b)2.69 x 10-4
- c)2.96 x 10-3
- d)2.69 x 10-3
Correct answer is option 'D'. Can you explain this answer?
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An intrinsic semiconducting sample has an energy gap of 0.38eV, calcul...
Given information:
- Energy gap of the intrinsic semiconducting sample: 0.38 eV
- Temperature: 1000°C
Calculating the probability:
To calculate the probability that the lowest level in the conduction band will be occupied, we need to use the Boltzmann distribution.
The Boltzmann distribution gives the probability of finding a particle in a specific energy state at a given temperature. It is given by the equation:
P(E) = exp(-E / kT)
where P(E) is the probability of finding a particle in energy state E, k is the Boltzmann constant, and T is the temperature in Kelvin.
Converting temperature from Celsius to Kelvin:
To use the Boltzmann distribution equation, we need to convert the temperature from Celsius to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
Therefore, the temperature in Kelvin is:
T(K) = 1000 + 273.15 = 1273.15 K
Calculating the probability:
Now, we can calculate the probability using the Boltzmann distribution equation. The energy gap is given as 0.38 eV. To convert this to Joules, we use the conversion factor:
1 eV = 1.602 x 10^-19 J
Therefore, the energy gap in Joules is:
E = 0.38 x 1.602 x 10^-19 J = 6.0976 x 10^-20 J
Now, substituting the values into the Boltzmann distribution equation:
P(E) = exp(-E / kT) = exp(-6.0976 x 10^-20 J / (1.381 x 10^-23 J/K * 1273.15 K))
Calculating this expression gives us:
P(E) ≈ 2.69 x 10^-3
Therefore, the probability that the lowest level in the conduction band will be occupied at 1000°C is approximately 2.69 x 10^-3.
Conclusion:
The correct answer is option 'D' - 2.69 x 10^-3.
- Energy gap of the intrinsic semiconducting sample: 0.38 eV
- Temperature: 1000°C
Calculating the probability:
To calculate the probability that the lowest level in the conduction band will be occupied, we need to use the Boltzmann distribution.
The Boltzmann distribution gives the probability of finding a particle in a specific energy state at a given temperature. It is given by the equation:
P(E) = exp(-E / kT)
where P(E) is the probability of finding a particle in energy state E, k is the Boltzmann constant, and T is the temperature in Kelvin.
Converting temperature from Celsius to Kelvin:
To use the Boltzmann distribution equation, we need to convert the temperature from Celsius to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
Therefore, the temperature in Kelvin is:
T(K) = 1000 + 273.15 = 1273.15 K
Calculating the probability:
Now, we can calculate the probability using the Boltzmann distribution equation. The energy gap is given as 0.38 eV. To convert this to Joules, we use the conversion factor:
1 eV = 1.602 x 10^-19 J
Therefore, the energy gap in Joules is:
E = 0.38 x 1.602 x 10^-19 J = 6.0976 x 10^-20 J
Now, substituting the values into the Boltzmann distribution equation:
P(E) = exp(-E / kT) = exp(-6.0976 x 10^-20 J / (1.381 x 10^-23 J/K * 1273.15 K))
Calculating this expression gives us:
P(E) ≈ 2.69 x 10^-3
Therefore, the probability that the lowest level in the conduction band will be occupied at 1000°C is approximately 2.69 x 10^-3.
Conclusion:
The correct answer is option 'D' - 2.69 x 10^-3.
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An intrinsic semiconducting sample has an energy gap of 0.38eV, calculate the probability at 1000C that the lowest level in the conduction band will be occupied.a)3.01 x 10-4b)2.69 x 10-4c)2.96 x 10-3d)2.69 x 10-3Correct answer is option 'D'. Can you explain this answer?
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An intrinsic semiconducting sample has an energy gap of 0.38eV, calculate the probability at 1000C that the lowest level in the conduction band will be occupied.a)3.01 x 10-4b)2.69 x 10-4c)2.96 x 10-3d)2.69 x 10-3Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about An intrinsic semiconducting sample has an energy gap of 0.38eV, calculate the probability at 1000C that the lowest level in the conduction band will be occupied.a)3.01 x 10-4b)2.69 x 10-4c)2.96 x 10-3d)2.69 x 10-3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An intrinsic semiconducting sample has an energy gap of 0.38eV, calculate the probability at 1000C that the lowest level in the conduction band will be occupied.a)3.01 x 10-4b)2.69 x 10-4c)2.96 x 10-3d)2.69 x 10-3Correct answer is option 'D'. Can you explain this answer?.
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