Question

An electron can be located with an error equal to 10^-10 what is the uncertainty it its momentum​

Answer 1

According to the HEISENBERG UNCERTAINITY PRINCIPLE:

∆X.∆P>=h/4π (FORMULA)

However in this case we have to take up the minimum accuracy failure or error condition since the answer of the question will give a value not a range.

Hence we use :

∆x.∆p=h/4π

Here ∆x=error in position, ∆p=error in momentum and h=planck constant = 6.626×10^-34

The error in position is clearly given as 10^-10m

so the ∆x=10^-10 m

now using the formula we get :

∆x .∆p = h/4π

10^-10 × ∆p = 6.626×10^-34 / 4×3.14

∆p = 6.626 ×10^-34/ 4×3.14 × 10^-10

∆p = 10^-23 × 0.52 kgms^-1

Thus we get the ans = 5.27 × 10^-24 kgms^-1

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