Find the binding energy in an atom of 3 He, which has a mass of 3.016030 amu.

hey everyone in this example, we're asked for an atom of beryllium nine with a mass of nine point oh 1 to 182 AM us. What is the binding energy. So to find the binding energy, we want to recall our formula for mass effect, which we should recall is represented by delta M. This is going to be set equal to our atomic number of our adam beryllium Z. Which is multiplied by the mass of hydrogen. Where we have an atomic mass number of one, an atomic number of one. This is then added to the difference between our mass number, which we recall is represented by the simple A subtracted from our atomic number which we recall is represented by the symbol Z. And then multiplied by the atomic mass of a neutron which has a mass number of one and atomic number zero. And then this is going to be subtracted from the mass of our isotope. So, plugging in what we know, we would say that delta M. Is equal to our atomic number of beryllium. We would recall to the periodic table and see that it has an atomic number equal to four, so Z is equal to four. And we would plug in four. We're going to multiply this by the massive hydrogen, which from our periodic tables will be a value of 1.783 AM. Use quickly the mass of hydrogen one. The prompt as nine. So we would have nine subtracted from our atomic number for beryllium which from the periodic table we would see is four. And then this is multiplied by our mass of our neutron. Which we should recall is a value of 1.00866 am use and then subtracted from the mass of our isotope. So I'm just going to make more room for that because that is given in the prompt as 24 or sorry it's equal to So we're going to take this entire portion here in our calculators. And this is going to give us a value of 0.62438 AM use. Now we want to recall that the binding energy should be in units of mega electron volts. So we're gonna multiplied by the following conversion factor to go from am use two mega electron volts. And we should recall that for one a.m. You we have 931.5 mega electron volts. Now we're able to cancel out am use we're left with mega electron volts as our final units. And what we're going to get is a value equal to 58.160997 mega. And sorry, that should be a capital m mega electron volts as our binding energy. So this here would be our final answer to complete this example. I hope that everything I explained was clear. If you have any questions, please leave them down below. And I will see everyone in the next practice video

Ch.20 - Radioactivity and Nuclear Chemistry

Tro - Chemistry: A Molecular Approach 4th Edition

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Ch.20 - Radioactivity and Nuclear Chemistry

Problem 87

Chapter 20, Problem 87

Find the binding energy in an atom of ³He, which has a mass of 3.016030 amu.

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Identify the components of the helium-3 nucleus: it contains 2 protons and 1 neutron.

Calculate the mass of the individual nucleons: the mass of a proton is approximately 1.007276 amu and the mass of a neutron is approximately 1.008665 amu.

Determine the total mass of the nucleons if they were separate: add the mass of 2 protons and 1 neutron.

Subtract the actual mass of the helium-3 nucleus (3.016030 amu) from the total mass of the separate nucleons to find the mass defect.

Convert the mass defect from amu to energy using Einstein's equation, \( E = \Delta m \cdot c^2 \), where \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It reflects the stability of the nucleus; a higher binding energy indicates a more stable nucleus. This energy can be calculated using the mass defect, which is the difference between the mass of the nucleus and the sum of the masses of its individual nucleons.

Mass Defect

The mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus itself. This discrepancy arises because some mass is converted into energy when nucleons bind together, according to Einstein's equation E=mc². The mass defect is crucial for calculating the binding energy of an atom.

Atomic Mass Unit (amu)

An atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of a carbon-12 atom. In nuclear physics, using amu allows for easier calculations of binding energy and mass defect, as it provides a consistent scale for comparing atomic and subatomic masses.