We can see that the uncertainty in the velocity of the electron would be at least 1.053 x 10¹⁹ m/s.
To calculate the uncertainty in the velocity of an electron within a given location, we can use Heisenberg's uncertainty principle.
According to the principle, the uncertainty in position (Δx) and the uncertainty in velocity (Δv) of a particle are related by the equation:
Δx × Δv ≥ h / (4π)
Where h is Planck's constant (approximately 6.626 x 10⁻³⁴ J·s).
Given that the electron is to be located within 5 x 10⁻⁵ A° (angstroms), we need to convert this value to meters. One angstrom is equal to 10⁻¹⁰ meters.
So, the uncertainty in position (Δx) would be:
Δx = 5 x 10⁻⁵ A° * 10⁻¹⁰ m/A° = 5 x 10⁻¹⁵ m
Now, we can substitute the values into the uncertainty principle equation and solve for the uncertainty in velocity (Δv):
(5 x 10⁻¹⁵ m) * Δv ≥ (6.626 x 10⁻³⁴ J·s) / (4π)
To solve for Δv, we need to rearrange the equation:
Δv ≥ (6.626 x 10⁻³⁴ J·s) / (4π * 5 x 10⁻¹⁵ m)
Calculating this expression gives us:
Δv ≥ 1.053 x 10¹⁹ m/s
Therefore, the uncertainty in the velocity of the electron would be at least 1.053 x 10¹⁹ m/s.