Neutron to Proton Ratio - Video Tutorials & Practice Problems
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Nuclear Stability
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Now when it comes to our neutron to proton ratio, we need to understand that determining the ratio of neutrons to protons, so n over c, is a major method for determining nuclear stability. Here we're going to say the closer an isotope is to its ratio, then the more stable its nucleus. So here we have atomic numbers, and based on the atomic number of your isotope, we have the ideal neutron to proton ratio. Here we're going to say if your atomic number is less than or equal to 20, then the ideal ratio between neutrons and protons is 1. If your proton your number of protons is 21 to 40, then the ideal ratio is 1.25. And then we're going to say if you're 41 to 83 then it jumps to 1.52. Here we see that the trend is as our atomic number increases, our number of protons increases, that the ratio also adjusts and increases as well. Now here we're going to say that above an atomic number of 83, because we didn't go any further than that, stable nuclei exist only momentarily and are prone to radioactive decay or emission reactions. So if you have an atomic number that's greater than 83, you could undergo beta decay or alpha decay, some type of positron emission, or even electron capture. Now here we're talking about bismuth 209. Bismuth is the element with the atomic number of 83. It's the heaviest element with stable non radioactive isotopes. So once we go beyond this mass of 209, we open up ourselves to the possibility of any types of emission or capture reactions when it comes to our isotopes. So just remember, we're going to say that the number of neutrons and protons, there's an ideal ratio between them based on the atomic number of any given isotope.
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example
Neutron-to-Proton Ratio Example
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Here it says, based on their neutron to proton ratio, which isotope possesses the most stable nucleus? So remember, if we're going to do neutron to proton ratio, remember that your number of neutrons is equal to your mass number, a, minus your atomic number, c. Here it's first important to determine the atomic numbers of each one of these isomers. You're looking on the periodic table, h would be 1. Here we'd have beryllium which is 4, carbon which is 6, and calcium which is 20. Here we do 3 minus 1, which gives us 2 neutrons, and then we have 1 proton because the atomic number is 1. So its ratio will be 2. Here for beryllium, it's 10 minus 4, which is 6, divided by 4, is going to be 1.2, so it's going to be 1.5. Then we're going to have 14 minuteus 6, which is 8, divided by 6, so this is 1.33. And then we're gonna have 41 minus 20 which is 21 divided by 20 which equals 1.05. Now if we also notice, we'd see that the atomic numbers are all equal to or less than 20. Remember, when it's equal to or less than 20, the ideal ratio is 1, 1 neutron to 1 proton. Remember, the closer an isotope is to their ideal ratio, the more stable their nucleus. Here, calcium 41 is the closest to 1 at 1.05, so option 2 will be our final answer.
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concept
Neutron-to-Proton Plot
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Now here when we talk about a neutron to proton plot, we're gonna say that this is a graphical representation of nucleons that depicts a stability line and the band or valley of stability. So we have a few definitions we need to cover here. So nucleons. Nucleons, nucleus, these are just the subatomic particles confined within the nucleus of an atom. And we know that within the atom, within the nucleus, we have what? We have neutrons and we have protons. The stability line, so this black line here, this is the straight line where the number of neutrons equals the number of protons. And if we're doing a neutron to proton ratio, if they're equal to each other, then this line is equal to 1. Now the band or valley of stability, this is the curved plot of different, and we're gonna say here nonradioactive, isotopes based on their proton, well, based on their neutron to proton ratio, right? So again, this green curved line is our Banner Valley of stability. If you're falling within there, you're going to be stable, you're not gonna be radioactive. And we're going to say that this black line, which is increasing exponentially here, is our stability line, which is equal to 1. Remember, nucleons, nucleus, that's just our protons and neutrons found within the nucleus.
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example
Neutron-to-Proton Ratio Example
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So here this example question states, which of all isotopes will lie to the left of the neutron to proton curve? Here we have zirconium 90, thorium 230, palladium 110 and mercury 200. Here, zirconium 90, its mass number is 90, looking on the periodic table, its atomic number is 40. This will mean that it has 40 protons and then 90-forty is 50 neutrons. Here our atomic number is the number of protons. So we have 40 protons and then we just trace up to 50, which is around here. We can see that that's not to the left of our neutron to proton curve, which is our band of stability, so this is out. Thorium 230, so we have 230 for the mass number for Thorium. Its atomic number is 90. We have 90 protons and then we're going to say here 230-forty, minus 90 is 140. So we have 90 and we just take it all the way up to 140 which is kind of off scale. So again, it's not to the left. Palladium 110. Palladium has an atomic number 46, so we have 46 protons and then here we're going to do 110-forty 6 here. So when we do that, we're going to get 64. So then here we have, let's see, 46, which is around here for protons and we just go up to about 64, which is going to put us about here. We're just slightly to the left. This seems to be our answer. Well, let's do the last one, Mercury 200, so 200 for mercury and its atomic number is 80. So we have 80 protons and we have 120 neutrons. So 80 and then we go up to 120, so we are going to be to the right of the curve. So option d does not work. Here, only option c is the correct answer.