Question

An electron has a speed of 500 m/s with an accuracy of 0.004%. Calculate the certainty with which we can locate the position of the electron.

a. 0.02 m
b. 0.04 m
c. 0.08 m
d. 0.16 m

Answer 1

OPTION A.According to the uncertainty principle, the certainty with which we can locate the position of an electron can be calculated using the uncertainty in its momentum. In this case, the certainty is approximately 0.207 x 10^-32 m.

Step-by-step explanation:

According to the uncertainty principle in quantum mechanics, the uncertainty in the position of an electron (Δx) is related to the uncertainty in its momentum (Δp) by the inequality Δx Δp ≥ ħ/2, where ħ is the reduced Planck's constant. To calculate the certainty with which we can locate the position of the electron, we need to find the minimum uncertainty in position.

Since the electron's speed is given as 500 m/s with an accuracy of 0.004%, we can calculate the uncertainty in momentum as Δp = (0.004/100) * (500 m/s) = 0.02 kg m/s. Therefore, the minimum uncertainty in position is given by Δx ≥ ħ/2Δp = (6.626 x 10^-34 Js)/(2*0.02 kg m/s) = 0.207 x 10^-32 m. So, the certainty with which we can locate the position of the electron is approximately 0.207 x 10^-32 m.