In: Physics
An electron and a 140-g baseball are each traveling 140 m/s measure to a precision of 0.055%.
A. Calculate the uncertainty in position of the electron.
B. Calculate the uncertainty in position of the baseball.
C. Compare the uncertainty in position of each.
Please label and circle answers. Express answers to 2 sigfigs and include units. Thanks!
To find the uncertainity in position, we use Heisenberg's uncertainity formula.
where
is the uncertainity in position
is the uncertainity in velocity
is Planck's Constant, equal to
This formula basically sets a lower bound to the amount of uncertainity in measurement of either the momentum or position. This means you can either know the position with great certainity, or the the momentum with great certainity, but not both at the same time. This is exemplified for smaller particles.
Part A
Since the speed is much lower than relativistic speeds, the uncertainity in momentum is only due to uncertainity in velocity.
where
Substituting our values, we get
Part B
Similarly, we calculate the uncertainity in position for the baseball.
Part C
The uncertainity for the electron is approximately 29 orders of magnitude larger. This implies that there is almost no uncertainity in position for the baseball, but there is a small but not negligible uncertainity in the position of the electron.
This is because uncertainity becomes more apparent on the quantum scale, and is negligible on a larger scale, such as the scale we exist on.