A pair of nuclei for which Z1=N2 and Z2=N1 are called mirror...

A pair of nuclei for which $Z_{1}=N_{2}$ and $Z_{2}=N_{1}$ are called mirror isobars. (The atomic and neutron numbers are interchangeable.) Binding - energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces. Charge independence means that the proton–proton, proton–neutron, and neutron–neutron forces are approximately equal. Calculate the difference in binding energy for the two mirror nuclei $^{15}_{8} \mathrm{O}$ and $_{7}^{15} \mathrm{N}$.

Key Concepts

Mirror Isobars

Mirror isobars are pairs of nuclei in which the number of protons in one nucleus equals the number of neutrons in the other and vice versa. This reflects a symmetry in their composition, allowing researchers to compare nuclei that have their charge distributions 'swapped.' The study of mirror isobars is an important tool in probing the underlying symmetries in nuclear structure, particularly related to how nuclear forces behave regardless of whether a nucleon is a proton or a neutron.

Binding Energy

Binding energy is the energy that holds a nucleus together, representing the difference between the total mass of the individual nucleons and the mass of the nucleus. It is a measure of the stability of the nucleus, with a higher binding energy indicating a more stable configuration. Differences in binding energy among nuclei provide insight into the forces at play within the nucleus and the interactions between protons and neutrons.

Charge Independence of Nuclear Forces

The charge independence of nuclear forces is the principle that the strong nuclear force acts nearly equally between any two nucleons, whether they are protons or neutrons. This means that the proton-proton, proton-neutron, and neutron-neutron interactions are approximately the same, apart from electromagnetic contributions. Comparing mirror isobars serves as an effective method for probing this independence by minimizing differences in nuclear structure while altering the proton and neutron composition.

Transcript

00:02 Number 13, we're asked to find the difference in the binding energy between these two atoms.

00:12 Remember what binding energy is.

00:14 If i would add up the mass of all the protons in an atom plus the mass of all the neutrons in the atom, that would be bigger than the overall mass.

00:27 So there's some mass missing.

00:29 That's the mass defect.

00:30 So the proton mass plus a neutron mass minus the mass of what i'm going to call the total.

00:39 The total mass of the element.

00:41 That's how much mass is missing.

00:43 And that is the binding energy.

00:46 So i looked up the mass of a proton here.

00:50 I looked up the mass of a neutron here.

00:52 So saved myself a little writing.

00:54 And then the total, you look this up in the back of the book in appendix b.

01:01 Okay, so the mass defect for this oxygen 15.

01:07 It has an atomic number of 8, so there's 8 protons.