The radius of an approximately spherical nucleus is given by r = A) r₀Z³. B) r₀Z^1/3. C) r₀A³. D) r₀A^1/3. E) r₀(A − Z)^1/3.

Question

Quizplus · Accepted Answer

The radius of a nucleus can be estimated using the empirical formula r = r0A^1/3, where r0 is a constant and A is the mass number of the nucleus. The constant r0 can be expressed as r0 = r₀A^-1/3, where rS, U, B, and P are constants that depend on the strong force, the electromagnetic force, the surface tension of the nucleus, and the asymmetry of the proton-neutron distribution. Plugging in the given values for hydrogen (Z=1, A=1), we can solve for r using the formula r = r0A^1/3 = r₀A^-1/3 * A^1/3 = r₀A^0 = r₀. Therefore, the radius of hydrogen is simply a constant, which tells us that the asymmetry term (A-Z) and the surface tension term (P) do not have any effect on the radius in the case of hydrogen. The only answer choice that does not include these terms is D, so it is the best choice.

The Radius of an Approximately Spherical Nucleus Is Given by R