Question

Rutherford's scattering experiments gave the first indications that an atom consists of a small, dense, positively charged nucleus surrounded by negatively charged electrons. His experiments also allowed for a rough determination of the size of the nucleus. In this problem, you will use the uncertainty principle to get a rough idea of the kinetic energy of a particle inside the nucleus. Consider a nucleus with a diameter of roughly 5.0×10−15 meters.

Part A: Consider a particle inside the nucleus. The uncertainty Δx in its position is equal to the diameter of the nucleus. What is the uncertainty Δp of its momentum? To find this, use ΔxΔp≥ℏ2.

Answer 1

ΔxΔp≥ℏ/2

Δx is the uncertainty in position and Δp is the uncertainty in momentum

ℏ = h/2$\pi$

5 * 10^-15 *Δp = 6.62*10^-34/4*3.14

Δp = 6.62*10^-34/4*3.14*5 * 10^-15

Δp = 1.05 * 10 ^ -20 kg m/s