A particle's position is known with an uncertainty of 0.01 nanometers. Calculate the minimum uncertainty in its velocity as described by Heisenberg's Uncertainty Principle.
Guide On Rating System
Vote
According to Heisenberg's Uncertainty Principle, the product of the uncertainty in position (Δx) and the uncertainty in velocity (Δv) must be greater than or equal to Planck's constant divided by 2π (h/2π):
Δx * Δv >= h/2π
Given that the uncertainty in position (Δx) is 0.01 nanometers, we can substitute this value into the equation:
0.01 nm * Δv >= h/2π
To find the minimum uncertainty in velocity, we need to rearrange the equation and solve for Δv:
Δv >= h / (0.01 nm * 2π)
Now we can substitute Planck's constant (h) into the equation, which is approximately 6.626 x 10^(-34) joule-seconds:
Δv >= (6.626 x 10^(-34) J·s) / (0.01 x 10^(-9) m * 2π)
Simplifying this expression:
Δv >= 6.626 x 10^(-25) J·s / (0.01 x 6.28 x 10^(-9) m)
Δv >= 6.626 x 10^(-25) / (0.0628 x 10^(-9))
Calculating this value:
Δv >= 1.053 x 10^6 m/s
Therefore, the minimum uncertainty in the particle's velocity is approximately 1.053 x 10^6 meters per second.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99