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The speed of an electron is measured to be 5.0 *103 m/s to an accuracy of 0.003%. Find the uncertainty (in m) in determining position of this electron.
Given : mass of electron = 9.11 x 10-31 kg
h = 6.63 *10-34Js
Given : mass of electron = 9.11 x 10-31 kg
h = 6.63 *10-34Js
Correct answer is '0.707'. Can you explain this answer?
Verified Answer
The speed of an electron is measured to be 5.0 *103 m/s to an accuracy...
The general condition of normalisation is
Here there are two terms. Thus
A* A + A* A = 1.
For real values, A = A*
A = 1/√2 .
Here there are two terms. Thus
A* A + A* A = 1.
For real values, A = A*
A = 1/√2 .
This question is part of UPSC exam. View all Physics courses
Most Upvoted Answer
The speed of an electron is measured to be 5.0 *103 m/s to an accuracy...
Given:
Speed of electron (v) = 5.0 x 10^3 m/s
Accuracy = 0.003% = 0.003/100 = 0.00003
Mass of electron (m) = 9.11 x 10^-31 kg
Planck's constant (h) = 6.63 x 10^-34 Js
To Find:
Uncertainty in determining the position of the electron (Δx)
Solution:
1. Uncertainty Principle:
The uncertainty principle states that it is impossible to simultaneously determine both the position and momentum (or velocity) of a particle with absolute precision. The product of uncertainties in position (Δx) and momentum (Δp) must be greater than or equal to the reduced Planck's constant (h/2π).
ΔxΔp ≥ h/2π
2. Calculating Uncertainty in Momentum:
The momentum (p) of an electron is given by the equation:
p = mv
where m is the mass of the electron and v is its velocity. Rearranging the equation, we can find the uncertainty in momentum (Δp) as:
Δp = mΔv
Since the accuracy is given as a percentage, we can calculate the uncertainty in velocity as:
Δv = (accuracy/100) * v
Substituting the values:
Δv = (0.00003) * (5.0 x 10^3)
Δv = 0.15
Δp = (9.11 x 10^-31) * (0.15)
Δp = 1.37 x 10^-31 kg·m/s
3. Calculating Uncertainty in Position:
Using the uncertainty principle equation:
ΔxΔp ≥ h/2π
we can rearrange the equation to solve for Δx:
Δx ≥ h/(2πΔp)
Substituting the values:
Δx ≥ (6.63 x 10^-34)/(2π * 1.37 x 10^-31)
Δx ≥ 0.707
Therefore, the uncertainty in determining the position of the electron is 0.707 meters.
Speed of electron (v) = 5.0 x 10^3 m/s
Accuracy = 0.003% = 0.003/100 = 0.00003
Mass of electron (m) = 9.11 x 10^-31 kg
Planck's constant (h) = 6.63 x 10^-34 Js
To Find:
Uncertainty in determining the position of the electron (Δx)
Solution:
1. Uncertainty Principle:
The uncertainty principle states that it is impossible to simultaneously determine both the position and momentum (or velocity) of a particle with absolute precision. The product of uncertainties in position (Δx) and momentum (Δp) must be greater than or equal to the reduced Planck's constant (h/2π).
ΔxΔp ≥ h/2π
2. Calculating Uncertainty in Momentum:
The momentum (p) of an electron is given by the equation:
p = mv
where m is the mass of the electron and v is its velocity. Rearranging the equation, we can find the uncertainty in momentum (Δp) as:
Δp = mΔv
Since the accuracy is given as a percentage, we can calculate the uncertainty in velocity as:
Δv = (accuracy/100) * v
Substituting the values:
Δv = (0.00003) * (5.0 x 10^3)
Δv = 0.15
Δp = (9.11 x 10^-31) * (0.15)
Δp = 1.37 x 10^-31 kg·m/s
3. Calculating Uncertainty in Position:
Using the uncertainty principle equation:
ΔxΔp ≥ h/2π
we can rearrange the equation to solve for Δx:
Δx ≥ h/(2πΔp)
Substituting the values:
Δx ≥ (6.63 x 10^-34)/(2π * 1.37 x 10^-31)
Δx ≥ 0.707
Therefore, the uncertainty in determining the position of the electron is 0.707 meters.
Community Answer
The speed of an electron is measured to be 5.0 *103 m/s to an accuracy...
The general condition of normalisation is
Here there are two terms. Thus
A* A + A* A = 1.
For real values, A = A*
A = 1/√2 .
Here there are two terms. Thus
A* A + A* A = 1.
For real values, A = A*
A = 1/√2 .
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The speed of an electron is measured to be 5.0 *103 m/s to an accuracy of 0.003%. Find the uncertainty (in m) in determining position of this electron.Given : mass of electron = 9.11 x 10-31 kgh = 6.63 *10-34JsCorrect answer is '0.707'. Can you explain this answer?
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