Question

An object is moving along a straight line and the uncertainty in its position is 1.1 m.

(a) Find the minimum uncertainty in the momentum of the object.

(b) Find the minimum uncertainty in the object's velocity, assuming that the object is a golf ball (mass = 0.045 kg).

(c) Find the minimum uncertainty in the object's velocity, assuming that the object is an electron.

Answer 1

Δx•Δp≥Һ/2
Δx•Δp=Һ/2
Δp = Һ/2• Δx = 6.63•10^-34/2•1.1 = 3•10^-34 kg•m/s,
Δp = m•Δv
Δv = Δp/m = 3•10^-34/0.045 = 6.7•10^-33 m/s,
Δv = Δp/m = 3•10^-34/9.1•10^-31 = 3.3•10^-4 m/s.

Answer 2

Using the Bohr model, estimate the wavelength ë of the Ká characteristic X-ray for a metal an atom of which contains Z = 50 protons.