The atomic mass of gold-197 is 196.96654 u. How much energy is required to completely separate t

step 1 Question 44. The atomic mass of gold 197 is 196 .9654U. How much energy is required to completel

The atomic mass of gold-197 is 196.96654 u. How much energy...

Key Concepts

Binding Energy

The binding energy is the energy required to completely disassemble a nucleus into its individual protons and neutrons. It represents the stability of the nucleus and is equivalent to the energy released when the nucleus was formed from these nucleons.

Mass Defect

The mass defect is the difference between the total mass of the individual nucleons (protons and neutrons) and the actual mass of the nucleus. This 'missing' mass has been converted into binding energy according to the mass-energy equivalence principle.

Mass-Energy Equivalence

Mass-energy equivalence, encapsulated by Einstein's equation E=mc², is the principle that mass can be converted into energy and vice versa. It provides the foundation for calculating the energy associated with the mass defect in nuclear reactions.

Atomic Mass Unit to Energy Conversion

This concept involves converting atomic mass units (u) into energy (typically expressed in mega-electron volts, MeV) using a specific conversion factor. This conversion is crucial for quantifying the energy corresponding to the mass defect in nuclear processes.

Transcript

00:01 Question 44.

00:02 The atomic mass of gold 197 is 196 .9654u.

00:08 How much energy is required to completely separate the nucleons in a gold 197 nucleus? so we're told the atomic mass that we're dealing with and the element that we're dealing with, or the atom that we're dealing with.

00:22 So we want to know how much energy will it take to separate this atom.

00:26 So in the scenario, we have a whole atom, and we want to separate them into its contingent opponents, all these little atoms separated.

00:36 So basically it's asking how much energy does it take to bind our nucleus together? so if this is the reaction that we're dealing with, our equation or our formula that we want to look for the energy to be, would be something like this.

00:52 We have 197.

00:55 It separates into protons and neutrons.

00:57 So we have a certain number of protons and a certain number of neutrons, we could say.

01:03 Where atomic number is 79, so we have 79 protons.

01:07 And the difference between the atomic mass and the geometric number is the number of protons, which in this case would be 118 neutrons.

01:18 So if we want to find the energy, we need our mass energy relationship, or just our energy is the change in mass, the net change in mass times c squared.

01:32 So our change in mass is the number of protons plus neutrons, minus the mass of the gold atom in general, right? so i'm going to type this out, just so it's a little clear.

01:43 So our change in mass, i'll just call mc, my own as little m subc, change in mass.

01:54 We have 79 protons, 79 times the mass of protons, times the mass of proton, which if we look up, it's found on this page.

02:04 Well, i put it here on this page, mass of the proton...

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