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 isoburs. (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 ${ }_{8}^{1} \mathrm{O}$ and ${ }_{7}^{15} \mathrm{~N}$.

Key Concepts

Charge Independence of Nuclear Forces

The charge independence of nuclear forces is the principle stating that the strong nuclear force between any two nucleons (proton-proton, neutron-neutron, or proton-neutron) is nearly identical. This concept is fundamental because it implies that the nuclear interaction does not depend on the individual charge of the nucleons, leading to symmetry patterns such as those observed in mirror nuclei. Studying the binding energy differences in mirror nuclei provides experimental evidence for this charge independence.

Mirror Nuclei

Mirror nuclei refer to a pair of nuclei in which the number of protons in one nucleus equals the number of neutrons in the other, and vice versa. This concept is important in nuclear physics because comparing such pairs helps scientists study symmetries in nuclear forces and understand how the interchange of protons and neutrons affects nuclear properties such as binding energy.

Binding Energy

Binding energy is the energy required to completely disassemble a nucleus into its individual protons and neutrons. It reflects the stability of the nucleus: a higher binding energy indicates a more stable nucleus. In nuclear physics, differences in binding energies between mirror nuclei can reveal subtle effects of the interactions among nucleons, including the influence of electromagnetic interactions and charge independence.

Transcript

00:01 Hello, and in this question here, we want to use the mirror nuclei to show that the interactions between the proton and the proton, the neutron and the proton and the neutron and the neutron for the strong nuclear force are approximately equal.

00:19 So to do this, we're going to use mirror nuclei.

00:24 And a mirror nuclei, well, what is that? okay, if we have two nuclei, we have first nucleus x.

00:30 And a second nucleus y.

00:33 Well, they're going to be mirror nuclei if the number of protons and the second atom is equal to a1 times the number of, so the number of nucleon.

00:44 So the mirror nuclei if the number of protons in the second atom equals the number of neutrons in the first atom.

00:51 So this quantity here is the number of neutrons, it's the number of nucleons minus the number of protons and that is the number of nucleons.

01:00 So they're mirror nuclei if the number of protons in the second atom equals the number of neutrons in the first atom and the number of protons in the first atom equals the number of neutrons in the second atom.

01:13 Okay.

01:13 And that there's the definition for mirror nuclei.

01:16 Two examples of mirror nuclei.

01:18 Well, we'd have oxygen 15, okay, and nitrogen 15.

01:26 So we can see here that oxygen 15 has eight protons and seven neutrons.

01:35 So the number of protons is equal to the number of neutrons in the nitrogen 15.

01:41 So let me just spell this out.

01:43 So there's eight protons, seven neutrons.

01:47 And there is seven protons, eight neutrons.

01:49 Okay, so the number of protons of oxygen is equal to the number of neutrons in the nitrogen, and the number of neutrons in the oxygen is equal to the number of protons in the nitrogen, and hence then, mirror a nuclei.

02:04 Okay.

02:05 So by comparing the binding energy, okay, we're going to show that the interaction is approximately the same...

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