Using a mass spectrometer, the mass of the 92^238 U^+ ion is found to be 238.05024 u. (a) Use t

Using a mass spectrometer, the mass of the 92^238 U^+ ion...

Key Concepts

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein’s equation E=mc², underpins the relationship between mass and energy. This principle allows the conversion of a mass defect (the difference between the sum of the individual masses of nucleons and the actual nucleus mass) into binding energy, providing insights into the stability and energy dynamics of atomic nuclei.

Mass Spectrometry

Mass spectrometry is an analytical technique used to measure the mass-to-charge ratio of ions. In the context of nuclear physics, it is employed to obtain accurate mass measurements of atomic or nuclear species, which are essential for further calculations such as determining binding energies or mass defects.

Atomic versus Nuclear Mass

The distinction between atomic mass and nuclear mass is fundamental in nuclear physics. An atomic mass typically includes the mass of the electrons surrounding the nucleus, whereas the nuclear mass refers only to the protons and neutrons. When analyzing nuclear properties, it is important to remove the electron masses from the atomic mass to isolate the mass of the nucleus alone.

Electron Mass Correction

Electron mass correction is the process of subtracting the combined mass of electrons from the atomic mass to determine the mass of the nucleus. This correction is crucial because the measured mass in techniques like mass spectrometry often includes the electrons, and accurate nuclear calculations require knowing just the mass of the nucleons.

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. It is derived from the mass defect and represents the energy that holds the nucleus together. The binding energy is a key concept in understanding nuclear stability, nuclear reactions, and energy generation in nuclear processes.

Transcript

00:01 Hello, and in this question here, we're going to determine the binding energy of the uranium 238 nucleus.

00:08 So we find out that the mass of the sum of the masses of all the individual nucleons is not equal to the mass of the nucleus.

00:20 And the difference is the binding energy.

00:24 So the binding energy is the amount of energy we would need to supply to the nucleus in order to break the nucleus.

00:31 Down into its individual nucleus.

00:35 So to calculate this binding energy, we are first given that the mass of the uranium 238 ion, so it's positively charged ion, is equal to 238 .05024u.

01:00 So what is this mass equal to? well, this mass of the ion is equal to the mass of the nucleus plus the mass of the electrons that are contained within this ion.

01:15 Okay? so how many electrons does this ion have? okay? well, we have, there will be 92 protons in uranium.

01:29 There will be 146 neutrons.

01:31 So to calculate 146, we have 92 protons.

01:38 We have 238 nucleons.

01:41 So 238 minus 92 is equal to 46.

01:45 146.

01:46 And these are the number of neutrons in this nucleus.

01:51 And for us to have a positive charge of plus 1, we must have one more proton than we do electrons.

01:58 So that means we must have 91 electrons.

02:01 Okay? so we now know that this value here that we're given is the mass of the nucleus plus the mass of 91 electrons.

02:11 We also ignore the binding energy of the electrons to the nucleus as this is very small compared to other contributions to the mass.

02:23 So this means the mass of the nucleus is equal to the mass of the ion minus the mass of the electrons...

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