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The uncertainty in position of an electron is equal to its de Broglie wavelength. The minimum percentage error in its measurement of velocity under this circumstance will be approximately.
- a)4
- b)8
- c)2
- d)18
Correct answer is option 'B'. Can you explain this answer?
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The uncertainty in position of an electron is equal to its de Broglie ...
Explanation:
Given:
Uncertainty in position, Δx = λ (de Broglie wavelength)
Percentage error in velocity measurement, Δv = ?
Formula:
Δx * Δv ≥ h / 4π (Heisenberg Uncertainty Principle)
Calculation:
Given, Δx = λ
Δx * Δv ≥ h / 4π
λ * Δv ≥ h / 4π
Δv ≥ h / (4πλ)
Percentage error in velocity measurement, Δv% = (Δv / v) * 100
Δv% = (h / (4πλv)) * 100
Since v = c (speed of light for an electron)
Δv% = (h / (4πλc)) * 100
Solving for minimum percentage error:
Δv% = (h / (4πλc)) * 100
Δv% = (h / (4π * λ * c)) * 100
Δv% = (h / (4π * λ * c)) * 100
Δv% = (h / (4π * λ * c)) * 100
Given λ = Δx = uncertainty in position
So, Δv% = (h / (4π * Δx * c)) * 100
Δv% = (h / (4π * λ * c)) * 100
Approximating the value of π as 3, we get:
Δv% = (h / (12λc)) * 100
Since h, λ, and c are constants, the minimum percentage error in velocity measurement will be approximately 8% (2 * 100 / 12). Therefore, the correct answer is option 'B'.
Given:
Uncertainty in position, Δx = λ (de Broglie wavelength)
Percentage error in velocity measurement, Δv = ?
Formula:
Δx * Δv ≥ h / 4π (Heisenberg Uncertainty Principle)
Calculation:
Given, Δx = λ
Δx * Δv ≥ h / 4π
λ * Δv ≥ h / 4π
Δv ≥ h / (4πλ)
Percentage error in velocity measurement, Δv% = (Δv / v) * 100
Δv% = (h / (4πλv)) * 100
Since v = c (speed of light for an electron)
Δv% = (h / (4πλc)) * 100
Solving for minimum percentage error:
Δv% = (h / (4πλc)) * 100
Δv% = (h / (4π * λ * c)) * 100
Δv% = (h / (4π * λ * c)) * 100
Δv% = (h / (4π * λ * c)) * 100
Given λ = Δx = uncertainty in position
So, Δv% = (h / (4π * Δx * c)) * 100
Δv% = (h / (4π * λ * c)) * 100
Approximating the value of π as 3, we get:
Δv% = (h / (12λc)) * 100
Since h, λ, and c are constants, the minimum percentage error in velocity measurement will be approximately 8% (2 * 100 / 12). Therefore, the correct answer is option 'B'.
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Community Answer
The uncertainty in position of an electron is equal to its de Broglie ...
By uncertainty principle
% uncertainty in velocity =
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