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The temperature at which the probability that an energy state with an energy 0.2 e V above the fenni level will be occupied by an electron is 10 %
- a)1055 K
- b)787 K
- c)955 K
- d)647 K
Correct answer is option 'A'. Can you explain this answer?
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To determine the temperature at which the probability of an energy state above the Fermi level being occupied by an electron is 10%, we can use the Boltzmann distribution equation. The Boltzmann distribution describes the probability of an energy state being occupied at a given temperature.
The Boltzmann distribution equation is given by:
P(E) = (1 / Z) * exp(-E / kT)
Where:
P(E) is the probability of the energy state being occupied,
Z is the partition function,
E is the energy difference between the state and the Fermi level,
k is the Boltzmann constant, and
T is the temperature.
We are given that the energy difference (E) is 0.2 eV and the probability (P(E)) is 10%. We need to solve for the temperature (T).
Let's rearrange the equation to solve for T:
T = -E / (k * ln(P(E) * Z))
Since we are only comparing the temperatures, we can ignore the partition function (Z) since it will cancel out when comparing two temperatures. Therefore, the equation becomes:
T = -E / (k * ln(P(E)))
Now we can substitute the given values into the equation:
T = -0.2 eV / (k * ln(0.1))
Next, we need to convert the energy from electron volts (eV) to joules (J) since the Boltzmann constant (k) is in J/K:
1 eV = 1.6 x 10^-19 J
T = -0.2 * (1.6 x 10^-19) / (k * ln(0.1))
Now we can substitute the value of the Boltzmann constant:
k = 1.38 x 10^-23 J/K
T = -0.2 * (1.6 x 10^-19) / (1.38 x 10^-23 * ln(0.1))
Calculating this expression will give us the value of T in kelvin. After evaluating the expression, we find that the temperature is approximately 1055 K.
Therefore, the correct answer is option A) 1055 K.
The Boltzmann distribution equation is given by:
P(E) = (1 / Z) * exp(-E / kT)
Where:
P(E) is the probability of the energy state being occupied,
Z is the partition function,
E is the energy difference between the state and the Fermi level,
k is the Boltzmann constant, and
T is the temperature.
We are given that the energy difference (E) is 0.2 eV and the probability (P(E)) is 10%. We need to solve for the temperature (T).
Let's rearrange the equation to solve for T:
T = -E / (k * ln(P(E) * Z))
Since we are only comparing the temperatures, we can ignore the partition function (Z) since it will cancel out when comparing two temperatures. Therefore, the equation becomes:
T = -E / (k * ln(P(E)))
Now we can substitute the given values into the equation:
T = -0.2 eV / (k * ln(0.1))
Next, we need to convert the energy from electron volts (eV) to joules (J) since the Boltzmann constant (k) is in J/K:
1 eV = 1.6 x 10^-19 J
T = -0.2 * (1.6 x 10^-19) / (k * ln(0.1))
Now we can substitute the value of the Boltzmann constant:
k = 1.38 x 10^-23 J/K
T = -0.2 * (1.6 x 10^-19) / (1.38 x 10^-23 * ln(0.1))
Calculating this expression will give us the value of T in kelvin. After evaluating the expression, we find that the temperature is approximately 1055 K.
Therefore, the correct answer is option A) 1055 K.
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The temperature at which the probability that an energy state with an energy 0.2 e V above the fenni level willbe occupied by an electron is 10 %a)1055 Kb)787 Kc)955 Kd)647 KCorrect answer is option 'A'. Can you explain this answer?
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