The radii of atomic nuclei are of the order of 5.0 Times 10^-15 m. Take this unc

Question

The radii of atomic nuclei are of the order of 5.0 Times 10^-15 m. Take this uncertainty in momentum to be an estimate of the magnitude of the momentum. Use the relativistic relationship between energy and momentum, equation E^2 = (mc^2)^2 + (pc)^2, to obtain an estimate of the kinetic energy of an electron confined within a nucleus. Calculate the magnitude of the Coulomb potential energy of a proton and an electron separated by r. Compare the energies calculated in parts B and C. On the basis of the result of part D, could there be electrons within the nucleus?

Explanation / Answer

by uncertainity principle

dx*dp>h/4pi

here dx = 5 x 10^-15m

dp > h/4pidx

dp = 1.056 x 10^-20 kg.m^2

pc = 3.1675 x 10^-12 J = 19.8 MeV

E^2 = (pc)^2 + (mc^2)^2 = (19.8MeV^2) + (0.511MeV^2)

E = 19.8 MeV

KE = E-mc^2 = 19.29 MeV

part c )

|U|<<K . K+|U| >> 0

part d )

no

K + U > 0 means the electron has enough energy to break from the bond

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