A proton is confined to a nucleus of radius 5 FM.what's the minimum uncertainty in momentum?
To find the minimum uncertainty in momentum, we can use the Heisenberg uncertainty principle, which states that the product of the uncertainties in position (Δx) and momentum (Δp) must be greater than or equal to a certain value.
The uncertainty in position (Δx) can be assumed to be equal to the size of the nucleus, which is given as the radius (r) of the nucleus. In this case, r = 5 FM (femtometers).
Now, to calculate the minimum uncertainty in momentum, we can use the formula:
Δp ≥ h / (4πΔx)
Where h is the Planck's constant (h ≈ 6.626 × 10^-34 Js).
Substituting the given values, we have:
Δp ≥ (6.626 × 10^-34 Js) / (4π(5 × 10^-15 m))
Simplifying this equation gives us:
Δp ≥ 1.328 × 10^-19 kg·m/s
Therefore, the minimum uncertainty in momentum of the proton confined to a nucleus with a radius of 5 femtometers is approximately 1.328 × 10^-19 kg·m/s.