Question

In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%, certainty with which the position of the electron can be located is: (h= 6.6×10⁻³⁴kgm²s⁻¹, mass of electron em=9.1×10⁻³¹Kg).

(A) 1.52×10−4m
(B) 5.01×10−3m
(C) 1.92×10−3m
(D) 3.84×10−3m

Answer 1

Using the Heisenberg Uncertainty Principle, the uncertainty in the position of an electron moving at 600 m/s with an accuracy of 0.005% is calculated to be approximately 3.84 x 10^-3 m.

Step-by-step explanation:

The student is asking about the Heisenberg Uncertainty Principle in Physics, which relates the uncertainty of an electron's position to its velocity. Given an electron's speed of 600 m/s with an accuracy of 0.005%, and using the provided Planck's constant and electron mass, we can calculate the certainty with which the position of the electron can be located.

First, we find Δv, the uncertainty in velocity, which is 0.005% of 600 m/s. This gives us Δv = 0.00005 × 600 m/s = 0.03 m/s.

Using the Heisenberg Uncertainty Principle formula (δx δp ≥ h/4π), where δx is the uncertainty in position and δp is the uncertainty in momentum, and knowing that δp = Δv × me, we can rearrange the formula to solve for δx:

δx ≥ σh / (4π × Δv × me)

Plugging in the values:

δx ≥ (6.6 × 10−34 kg m2 s−1) / (4π × 0.03 m/s × 9.1 × 10−31 kg)

After the calculation, we obtain δx ≥ 3.84 × 10−3 m, which is the uncertainty of position.