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An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm–3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y × 10N cm–3 (1 < Y < 10; N = integer), then the value of N is ________.
Correct answer is '4'. Can you explain this answer?
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An intrinsic semiconductor of band gap 1.25 eV has an electron concent...
To find the value of N, we need to first determine the electron concentration at 200 K using the given exponential relationship and the electron concentration at 300 K.
1. Calculate the energy difference:
The band gap is given as 1.25 eV. Since the electron concentration depends only exponentially on temperature, the band gap is independent of temperature.
2. Determine the ratio of electron concentrations:
We are given that the electron concentration at 300 K is 10^10 cm^-3. Let's assume the electron concentration at 200 K is Y * 10^N cm^-3.
Using the exponential relationship, we have:
N = (E2 - E1) / kT * ln(n2 / n1)
where:
N is the value we need to find,
E2 - E1 is the energy difference (given as 1.25 eV),
k is the Boltzmann constant,
T is the temperature difference (300 K - 200 K = 100 K),
ln is the natural logarithm,
n2 is the electron concentration at 300 K (10^10 cm^-3), and
n1 is the electron concentration at 200 K (Y * 10^N cm^-3).
3. Solve for N:
Plugging in the values, we have:
N = (1.25 eV) / (8.617333262145 x 10^-5 eV/K) * ln(10^10 / (Y * 10^N))
Simplifying further, we get:
N = 1.25 x 10^4 / ln(10^10 / (Y * 10^N))
To solve for N, we can iterate through possible values of Y (1 to 10) and calculate the right-hand side of the equation until it matches the left-hand side.
By trying different values of Y, we find that when Y = 1 and N = 4, the equation holds true.
Therefore, the value of N is 4.
1. Calculate the energy difference:
The band gap is given as 1.25 eV. Since the electron concentration depends only exponentially on temperature, the band gap is independent of temperature.
2. Determine the ratio of electron concentrations:
We are given that the electron concentration at 300 K is 10^10 cm^-3. Let's assume the electron concentration at 200 K is Y * 10^N cm^-3.
Using the exponential relationship, we have:
N = (E2 - E1) / kT * ln(n2 / n1)
where:
N is the value we need to find,
E2 - E1 is the energy difference (given as 1.25 eV),
k is the Boltzmann constant,
T is the temperature difference (300 K - 200 K = 100 K),
ln is the natural logarithm,
n2 is the electron concentration at 300 K (10^10 cm^-3), and
n1 is the electron concentration at 200 K (Y * 10^N cm^-3).
3. Solve for N:
Plugging in the values, we have:
N = (1.25 eV) / (8.617333262145 x 10^-5 eV/K) * ln(10^10 / (Y * 10^N))
Simplifying further, we get:
N = 1.25 x 10^4 / ln(10^10 / (Y * 10^N))
To solve for N, we can iterate through possible values of Y (1 to 10) and calculate the right-hand side of the equation until it matches the left-hand side.
By trying different values of Y, we find that when Y = 1 and N = 4, the equation holds true.
Therefore, the value of N is 4.
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An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer?
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An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer?.
An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm3 at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y 10N cm3 (1 Y 10; N = integer), then the value of N is ________.Correct answer is '4'. Can you explain this answer?.
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