The peak of the stability curve occurs at ^56 Fe, which is why iron is prominent in the spectrum

The peak of the stability curve occurs at ^56 Fe, which is...

The peak of the stability curve occurs at $^{56} \mathrm{Fe},$ which is why iron is prominent in the spectrum of the Sun and stars. Show that $^{56} \mathrm{Fe},$ has a higher binding energy per nucleon has a higher binding energy per nucleon than its neighbors $^{55} \mathrm{Mn}$ and $^{59} \mathrm{Co}$. Compare your results with Figure 29.4.

Key Concepts

Nuclear Binding Energy

This concept refers to the energy required to disassemble a nucleus into its individual protons and neutrons. It is a measure of the stability of a nucleus, with higher binding energy indicating a more stable structure. In nuclear processes, changes in binding energy per nucleon are fundamental in understanding the energy released or absorbed during reactions such as fusion and fission.

Binding Energy per Nucleon

Binding energy per nucleon is the average energy that holds each nucleon (proton or neutron) in the nucleus. It is calculated by dividing the total binding energy of the nucleus by the number of nucleons. This value is crucial in comparing the stability of different nuclei, with a higher binding energy per nucleon generally corresponding to greater stability.

Nuclear Stability Curve

The nuclear stability curve, often depicted as a plot of binding energy per nucleon versus mass number, illustrates how nuclear stability varies with the size of the nucleus. The curve typically peaks near iron, indicating that nuclei around this mass number have the highest binding energy per nucleon and are thus the most stable. This peak explains why certain nuclei, like iron-56, are particularly favored in the context of stellar nucleosynthesis and energy considerations in nuclear reactions.

Transcript

00:01 For number 14, we're to find the binding energy per nucleon for each of these elements.

00:07 Let's remember what that is.

00:09 You can find the mass defect, how much mass is missing by adding up the mass of the individual pieces.

00:18 So the mass of all the protons plus the mass of all the neutrons.

00:26 Those together are always a little bit more than the mass of the overall atom combined.

00:32 So i'm calling that mass total.

00:37 And that's something you can look up in appendix b in the back of the book.

00:43 So that missing mass is the binding energy.

00:46 So we'll calculate that mass in u's atomic mass units and then convert it to energy.

00:54 So here, i read my equation all set up here.

00:57 This is the mass of a proton in use.

00:59 This is the mass of one neutron in use.

01:02 So we're given iron 56.

01:05 So i can tell on a periodic table that the atomic number is 26.

01:10 So that means it has 26 protons.

01:15 And mass number remembers the sum of protons and neutrons.

01:19 So i subtract and i get that it has 30 neutrons.

01:23 And then i looked up on the table, iron 56, and that is 55 .934.

01:40 I do that math and i get that there is a mass defect of 0 .5 to 846 and that is measured in u atomic mass unit.

02:04 I'm gonna convert that.

02:06 I'm gonna convert that to the energy equivalent i know that 1 u is the same as 931 .5 mega electron volts so my u cancels.

02:29 So my binding energy is 492 .26 mega electron volts...

Please give Ace some feedback