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Diffusion constant (Dn) and mobility constant (μn) of an electron are related as follows
Dn/μn = KxTyqz
Where x, y, z are constants and ‘K’ is Boltzmann constant, ‘T’ is temperature, ‘q’ is charge of an electron.
Find the value of x+y+z.
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Diffusion constant (Dn) and mobility constant (μn) of an electron are...
We have, by Einstein’s Relation
Dn/μn = KT/q
Thus, x = 1,y = 1,z = -1
X + Y + Z = 1
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Diffusion constant (Dn) and mobility constant (μn) of an electron are...
To find the values of x, y, and z in the equation Dn/μn = KxTyqz, we can analyze the dimensions of each term in the equation.
1. Analyzing the dimensions of Dn:
- The diffusion constant (Dn) represents the rate at which electrons diffuse in a material.
- Diffusion is a process that occurs over a distance (length) and time.
- Therefore, the dimensions of Dn are [length^2/time].
2. Analyzing the dimensions of μn:
- The mobility constant (μn) represents the velocity of electrons in response to an electric field.
- Velocity is a distance (length) traveled per unit time.
- Therefore, the dimensions of μn are [length^2/(time*electric field)].
3. Analyzing the dimensions of K:
- The Boltzmann constant (K) is a physical constant representing the relationship between temperature and energy.
- The dimensions of K are [energy/(temperature)].
4. Analyzing the dimensions of T:
- Temperature (T) is measured in Kelvin (K).
5. Analyzing the dimensions of q:
- The charge of an electron (q) is a fundamental physical constant.
- The dimensions of q are [charge].
Now, let's equate the dimensions on both sides of the equation:
On the left-hand side (LHS):
- Dimensions of Dn/μn = [length^2/time] / [length^2/(time*electric field)] = [electric field]
On the right-hand side (RHS):
- Dimensions of KxTyqz = [energy/(temperature)] * [temperature]^x * [charge]^z
To equate the dimensions, the RHS must also have dimensions of [electric field]. This implies:
- [energy/(temperature)] * [temperature]^x * [charge]^z = [electric field]
Looking at each term separately:
- [energy/(temperature)] represents [electric field] if x = 1.
- [temperature]^x represents [electric field] if x = 0.
- [charge]^z represents [electric field] if z = 1.
Therefore, the values of x, y, and z are:
- x = 1
- y can be any value since it does not affect the dimensions.
- z = 1
Hence, the correct answer is option B) 1.
1. Analyzing the dimensions of Dn:
- The diffusion constant (Dn) represents the rate at which electrons diffuse in a material.
- Diffusion is a process that occurs over a distance (length) and time.
- Therefore, the dimensions of Dn are [length^2/time].
2. Analyzing the dimensions of μn:
- The mobility constant (μn) represents the velocity of electrons in response to an electric field.
- Velocity is a distance (length) traveled per unit time.
- Therefore, the dimensions of μn are [length^2/(time*electric field)].
3. Analyzing the dimensions of K:
- The Boltzmann constant (K) is a physical constant representing the relationship between temperature and energy.
- The dimensions of K are [energy/(temperature)].
4. Analyzing the dimensions of T:
- Temperature (T) is measured in Kelvin (K).
5. Analyzing the dimensions of q:
- The charge of an electron (q) is a fundamental physical constant.
- The dimensions of q are [charge].
Now, let's equate the dimensions on both sides of the equation:
On the left-hand side (LHS):
- Dimensions of Dn/μn = [length^2/time] / [length^2/(time*electric field)] = [electric field]
On the right-hand side (RHS):
- Dimensions of KxTyqz = [energy/(temperature)] * [temperature]^x * [charge]^z
To equate the dimensions, the RHS must also have dimensions of [electric field]. This implies:
- [energy/(temperature)] * [temperature]^x * [charge]^z = [electric field]
Looking at each term separately:
- [energy/(temperature)] represents [electric field] if x = 1.
- [temperature]^x represents [electric field] if x = 0.
- [charge]^z represents [electric field] if z = 1.
Therefore, the values of x, y, and z are:
- x = 1
- y can be any value since it does not affect the dimensions.
- z = 1
Hence, the correct answer is option B) 1.
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Diffusion constant (Dn) and mobility constant (μn) of an electron are related as followsDn/μn = KxTyqzWhere x, y, z are constants and ‘K’ is Boltzmann constant, ‘T’ is temperature, ‘q’ is charge of an electron.Find the value of x+y+z.a)0b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?
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