Question

Uncertainty in the position of an electron moving with a velocity 300 m/s accurate up to 0.001%, will be

1. 1.93 × 10⁻³ m
2. 1.93 × 10⁻² m
3. 3.86 × 10⁻² m
4. 3.86 × 10⁻³ m

Answer 1

The uncertainty in the position of an electron moving with a velocity of 300 m/s accurate up to 0.001% is approximately 1.93 × 10^-3 m. Option 1 is correct.

Step-by-step explanation:

The uncertainty in the position of an electron can be determined using the Heisenberg Uncertainty Principle, which states that there is a fundamental limit to how precisely we can know both the position and momentum of a particle at the same time.

The uncertainty in position (Δx) multiplied by the uncertainty in momentum (Δp) must be greater than or equal to Planck's constant divided by 4π (h/4π). This can be expressed as the equation Δx Δp ≥ h/4π.

In this case, the velocity of the electron is accurate up to 0.001%. To find the uncertainty in position, we can use the equation Δx Δp ≥ h/4π and rearrange it to solve for Δx. The uncertainty in momentum (Δp) can be approximated as the mass of the electron (m) multiplied by the uncertainty in velocity (Δv).

Using the given values, we can calculate the uncertainty in position:

Δx Δp = h/4π
Δx (m Δv) = h/4π
Δx = (h/4π) / (m Δv)
Δx = (6.626 × 10^-34 kg m^2/s) / (4π (9.11 × 10^-31 kg) (0.00001 * 300 m/s))
Δx ≈ 1.93 × 10^-3 m