Neutron to Proton Ratio - Online Tutor, Practice Problems & Exam Prep

Understanding the neutron to proton ratio (N/Z) is crucial for assessing nuclear stability. Isotopes with atomic numbers up to 20 have an ideal N/Z ratio of 1, while those with atomic numbers between 21 and 40 have a ratio of 1.25, and those between 41 and 83 have a ratio of 1.5. Isotopes with atomic numbers greater than 83 are inherently unstable and likely to undergo radioactive decay processes such as beta decay, alpha decay, positron emission, or electron capture. Bismuth-209, with an atomic number of 83, is the heaviest element with stable non-radioactive isotopes. The neutron to proton plot is a graphical tool that illustrates nucleons (protons and neutrons in the nucleus) and delineates the stability line (where N/Z = 1) and the band or valley of stability, where non-radioactive isotopes fall according to their N/Z ratio. Isotopes within this band are stable and non-radioactive.

Nuclear Stability

Now when it comes to our neutron to proton ratio, we need to understand that determining the ratio of neutrons to protons, so nZ, 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 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, and the ratio also adjusts and increases as well.

Now here we're going to say that above an atomic number of 83, 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 has an ideal ratio between them based on the atomic number of any given isotope.

Neutron-to-Proton Ratio Example

Here it says based on their neutron to proton ratio, which isotope possesses the most stable nucleus. So remember we're going to do neutron of proton ratio. Remember that your number of neutrons is equal to your mass number A minus your atomic number Z. Here it's first important to determine the atomic numbers of each one of these isotopes. 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 3-1, which gives us 2 neutrons, and then we have one proton because the atomic number is 1, so it's ratio B2 here. For Beryllium, it's 10-4, which is 6/4 is going to be 12, so it's going to be 15. Then we're going to have 14-6, which is 8/6, so this is 1.33. And then we're going to have 41-20 which is 21/20 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 11 neutron to one proton. Remember, the closer an isotope is to their ideal ratio, the more stable their nucleus. Here Calcium 41 is the closest to one at 1.05 O. Option 2 will be our final answer.

Neutron-to-Proton Plot

Now here when we talk about a neutron to proton plot, we're going to 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 going to say here non-radioactive isotopes based on their proton, well based on their neutron to proton ratio, right? So again, this green curved line is our band or valley of stability. If you're falling within there, you're going to be stable, you're not going to 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. And remember nucleons, nucleus? That's just our protons and neutrons found within the nucleus.

Neutron-to-Proton Ratio Example

So here this example question states which the following isotopes will lie to the left of the neutron to proton curve. Here we have Zirconium 90, Thorium 230, Palladium 110 and Mercury 200.

So here Zirconium 90 its mass number is 90. Looking on the periodic table its atomic number is 40. This would mean that it has 40 protons and then 90 - 40 is 50. Neutrons here are 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 - 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 - 46 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. So we're just slightly to the left. So this seems to be our answer, but 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're going to be to the right of the curve. So option D does not work here. Only option C is the correct answer.

Here’s what students ask on this topic:

Why is the neutron to proton ratio so important?

The neutron to proton ratio in an atomic nucleus is crucial because it directly influences the stability of the atom. Protons, being positively charged, repel each other due to the electrostatic force. Neutrons, which are neutral, help to mitigate this repulsion by providing an attractive force known as the strong nuclear force, which works over short distances within the nucleus.

For lighter elements (up to Iron), a roughly equal number of neutrons and protons can maintain a stable nucleus. However, as atoms get larger, more neutrons are required relative to protons to counterbalance the increasing electrostatic repulsion between the greater number of protons. If the neutron to proton ratio is too low or too high, the nucleus becomes unstable, leading to radioactive decay as the atom seeks a more stable configuration. This decay can result in the emission of particles and energy, transforming the atom into a different element or isotope. Understanding this ratio is essential in fields like nuclear physics, chemistry, and various applications such as nuclear energy and medical imaging.

For which of the following isotopes is the neutron-to-proton ratio greater than one?

To determine if an isotope has a neutron-to-proton (n/p) ratio greater than one, you need to compare the number of neutrons to the number of protons in the nucleus of the isotope. The number of protons is equivalent to the atomic number (Z), and the number of neutrons can be found by subtracting the atomic number from the mass number (A), which is the sum of protons and neutrons.

The neutron-to-proton ratio is calculated as:

$\frac{A-Z}{Z}$

If this ratio is greater than one, it means there are more neutrons than protons in the isotope.

For example, carbon-14 (with 6 protons and 8 neutrons) has a n/p ratio of:

$\frac{14-6}{6}=\frac{8}{6}\approx 1.33$

which is greater than one. So, carbon-14 would be an isotope with a neutron-to-proton ratio greater than one.

To apply this to any isotope, simply use the mass number and atomic number to calculate the ratio and check if it is greater than one.

How is each type of radioactive decay classified according to how it affects the neutron-to-proton ratio?

Radioactive decay can be classified into several types based on how it affects the neutron-to-proton (n/p) ratio in an atomic nucleus:

1. Alpha decay: This involves the emission of an alpha particle, which consists of two protons and two neutrons. Since the nucleus loses two protons, the atomic number decreases by two, and the atomic mass decreases by four. This process decreases the n/p ratio because it removes two neutrons for every two protons.
2. Beta-minus decay: In beta-minus decay, a neutron is transformed into a proton, and an electron (beta particle) and an antineutrino are emitted. The atomic number increases by one (since a proton is added), but the atomic mass remains the same. This decreases the n/p ratio because a neutron is converted into a proton.
3. Beta-plus decay (positron emission): Here, a proton is converted into a neutron, and a positron (the electron's antiparticle) and a neutrino are emitted. The atomic number decreases by one (since a proton is lost), but the atomic mass stays constant. This increases the n/p ratio because a proton is converted into a neutron.
4. Electron capture: Similar to beta-plus decay, a proton in the nucleus captures an orbiting electron and converts into a neutron, emitting a neutrino. The atomic number decreases by one, but the atomic mass remains the same. This increases the n/p ratio because a proton is converted into a neutron.

Which types of processes are likely when the neutron-to-proton ratio in a nucleus is too large?

When the neutron-to-proton (n/p) ratio in a nucleus is too large, the nucleus is considered neutron-rich and is unstable. To regain stability, such a nucleus will undergo radioactive decay processes that decrease the number of neutrons or increase the number of protons. The most common processes are:

1. Beta minus (β^-) decay: In this process, a neutron is transformed into a proton while emitting an electron (beta particle) and an antineutrino. This increases the proton count and decreases the neutron count, thus reducing the n/p ratio.
2. Electron capture: The nucleus captures one of its own electrons, usually from the closest shell to the nucleus, which then combines with a neutron to form a proton and an electron neutrino. This also increases the number of protons and decreases the number of neutrons in the nucleus.

Both of these processes are ways that a nucleus with too many neutrons can adjust its n/p ratio to become more stable.