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An electron has a speed of 100 m/s with an accuracy of 0.005%. The uncertainty in position will be in x meter,
the value of x is ?
the value of x is ?
Correct answer is '0.14'. Can you explain this answer?
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An electron has a speed of 100 m/s with an accuracy of 0.005%. The unc...
Uncertainty in Position Calculation:
- The uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of properties of a particle, such as position and momentum, can be known simultaneously.
- The uncertainty in position (∆x) can be calculated using the formula: ∆x = h / (4πm∆v), where h is the Planck constant, m is the mass of the electron, and ∆v is the uncertainty in velocity.
Given Values:
- Velocity of the electron (v) = 100 m/s
- Accuracy of velocity (∆v) = 0.005% = 0.00005 * 100 = 0.005 m/s
Calculation:
- Mass of an electron (m) = 9.11 x 10^-31 kg
- Planck constant (h) = 6.626 x 10^-34 J*s
- ∆x = (6.626 x 10^-34) / (4 * π * 9.11 x 10^-31 * 0.005) = 0.14 meters
Therefore, the uncertainty in position of the electron is 0.14 meters.
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