Final answer:
The least possible uncertainty in the speed of an electron in a helium atom is determined by the Heisenberg Uncertainty Principle and is calculated based on the atom's radius and the electron's mass and velocity. It's expressed as a percentage of the average electron speed.
Step-by-step explanation:
To calculate the least possible uncertainty in a measurement of the speed of an electron in a helium atom, we can use the Heisenberg Uncertainty Principle. According to this principle, the product of uncertainties in position (Δx) and momentum (Δp) of a particle is at least as large as the reduced Planck constant divided by 2, which mathematically is Δx Δp ≥ į/2.
For the electron in a helium atom orbiting with an average speed, we assume the uncertainly in position is roughly the size of the atom. With a helium atom radius of 31 pm (3.1 × 10-11 m), and using the reduced Planck constant (į), we can find the uncertainty in momentum.
The equation for the uncertainty principle is Δx Δp ≥ į/2. First we calculate the uncertainty in momentum (Δp), which is į/(2Δx). Then, since momentum (p) is the product of mass (m) and velocity (Δv), we can find the uncertainty in velocity (Δv) as Δp/m. The mass (m) would be the mass of an electron. Finally, to get the percentage of the average speed, we divide the uncertainty in velocity (Δv) by the average velocity (≤ 4.4 × 106 m/s) and multiply by 100%.