Question

If an electron has a wavelength ( λ ) and an uncertainty in its kinetic energy equal to ( Δ E ), what will be the uncertainty in its position?

a) ( Δ x = h/4π )

b) ( Δ x = h/2π )

c) ( Δ x = h/λ )

d) ( Δ x = λ/h )

Answer 1

The uncertainty in position (Δx) of an electron can be calculated using the equation Δx = h/Δp, where h is Planck's constant and Δp is the uncertainty in momentum. Therefore, option (b) Δx = h/2π is the correct answer.

Step-by-step explanation:

According to Heisenberg's uncertainty principle, the uncertainty in position (Δx) and the uncertainty in momentum (Δp) of an electron are related. The product of the uncertainties is approximately equal to Planck's constant (h), which is expressed as Δx * Δp ~ h. As the uncertainty in momentum is related to the wavelength (λ) of the electron, we can calculate the uncertainty in position by rearranging the equation as Δx = h/Δp, which is option (b) Δx = h/2π.