Uncertainty in the position of an electron (mass = 9.1 x 10-31 kg) moving with a velocity 300m/s accurate up to 0.001% will be

To solve this problem, we need to use Heisenberg's Uncertainty Principle, which states that the more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa. The principle is often stated as:

Δx * Δp ≥ h/4π

where:

• Δx is the uncertainty in position,
• Δp is the uncertainty in momentum,
• h is Planck's constant (6.626 x 10^-34 Js).

First, we need to calculate the uncertainty in velocity (Δv). Given that the velocity is known up to an accuracy of 0.001%, we can calculate Δv as:

Δv = 0.001/100 * 300 m/s = 0.003 m/s

Next, we calculate the uncertainty in momentum (Δp) using the formula Δp = m * Δv, where m is the mass of the electron:

Δp = 9.1 x 10^-31 kg * 0.003 m/s = 2.73 x 10^-33 kg m/s

Finally, we substitute Δp into the Heisenberg's Uncertainty Principle to find Δx:

Δx ≥ h/4πΔp = 6.626 x 10^-34 Js / (4π * 2.73 x 10^-33 kg m/s) = 0.000000000000000000000000000000000192 m

So, the uncertainty in the position of the electron is approximately 1.92 x 10^-34 m.