Indicate whether each of the following nuclides lies within the belt of stability in Figure 21.2: (a) neon-24. For any that do not, describe a nuclear decay process that would alter the neutron-to-proton ratio in the direction of increased stability. [Section 21.2]

Question

Indicate whether each of the following nuclides lies within the belt of stability in Figure 21.2: (a) neon-24. For any that do not, describe a nuclear decay process that would alter the neutron-to-proton ratio in the direction of increased stability. [Section 21.2]

Graph showing neutron-to-proton ratio and stability for nuclides in nuclear chemistry.

Accepted Answer

Welcome back everyone does. Argon 40. New glide lie within the band of stability shown in the image below. If not, how would you change the neutron to proton ratio for the nuclei to increase its stability. So looking at our graph below, we can see that our band of stability is defined by these red dots here and it's defined by a value equal to one of our proton to neutron ratio. So recognize that this equation here tells us that if we take the difference between our mass number from our number of protons divided by our number of protons, we should have a band of stability value or ratio rather of protons to neutrons equal to a value of one point. Oh, oh we know that our values E tells us our number of protons. Because we can see on the bottom of our plot the X axis records atomic number represented by the symbol Z. Which we recall tells us our number of protons. And so thinking of our isotope argon 40. We want to recall that argon on our periodic table corresponds to a atomic number or Z value of 18. So we would say Z is equal to 18, which tells us that we therefore have 18 protons. And so checking out this calculation, we take the mass number of argon which we know is represented by the left hand subscript or by the name of the isotope 40 here. Argon 40. So we would have for our neutron to proton ratio. We're going to take the mass number of 40 subtracted from our protons from the atomic number of argon on the periodic table divided by 18. And let's see what value this gives us. So this is going to equal a value of 1.2222. And so we would say that our neutron to proton ratio for argon 40 Which is 1. is greater than 1.0, which is what we need for our band of stability. And so we would say therefore Argon lies just above the band of stability and has too many neutrons. We know that because we recall that our mass number of 40 is calculated from our number of protons plus our number of neutrons. And in in our numerator, we take our difference between our mass number and our number of protons 18 to give us our number of neutrons. So we know that since our ratio of protons to neutrons is greater than one for our band instability, we know we have too many neutrons and so to get rid of these excess neutrons. So to we'll say to mend this access of neutrons, we should lower the proton two neutron ratio. So it will say the NZ ratio to keep things consistent via beta decay. And we know that we should use beta decay because looking at our plot, we see that beta decay is associated with neutron emission, meaning we would lose neutrons. We would get rid of those excess neutrons and lowering our neutron to proton ratio via beta decay will say, will increase, we'll say this will increase Argon forty's stability. So for our final answer will confirm that Argon 40 lies just above the band of stability. And because of its excess neutrons, we should lower the proton to neutron ratio via beta decay. And this will increase Argon forty's stability. So what's highlighted in yellow is our final answer. I hope what I went through is clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

Indicate whether each of the following nuclides lies within the belt of stability in Figure 21.2: (a) neon-24. For any that do not, describe a nuclear decay process that would alter the neutron-to-proton ratio in the direction of increased stability. [Section 21.2]

Verified Solution

Key Concepts

Belt of Stability

Neutron-to-Proton Ratio

Types of Nuclear Decay