# How to tell if an isotope is radioactive

My teacher said that if an isotope has a neutron to proton ratio that is greater than 1.2 it is radio active, but he said there is one exception when the ratio is lower than 1.2 .. something about the isotope being synthetic. Can someone help me an explain exactly what this exception is.

Thank you.

Btw i originally posted this question in the chemistry section and was referred here.

Hydrogen comes to mind, since it can consist of only one proton and no neutrons. A few other lighter elements can exist in a stable state without obeying a 1.2 neutron/proton ratio. Look here: http://www.nndc.bnl.gov/chart/

Also, I'm sure sure how synthetic isotopes come into this topic. Of course I'm sure isotopes that don't follow the ratio can also be created.

Astronuc
Staff Emeritus
My teacher said that if an isotope has a neutron to proton ratio that is greater than 1.2 it is radio active, but he said there is one exception when the ratio is lower than 1.2 .. something about the isotope being synthetic. Can someone help me an explain exactly what this exception is.
Is the teacher quoted correctly?

One can look at the chart of nuclides (see the link that theCandyman cited) and see that there a many radioisotopes with n/p < 1. Those radionuclides with n/p closer to 1 would tend to decay by positron emission, e.g. Sc-44, with n/p ~1.09.

Sc-46 has n/p ~ 1.19 and decays by beta decay.

The heaviest stable nuclide with n/p=1 is Ca-40. Beyond that the stable isotopes have n/p > 1.

Ni-58 has the next lowest n/p (~ 1.071) of stable isotopes above Ca.

Ca-46 and Ca-48 have n/p of 1.3 and 1.4 respectively, but are stable.

Now He-3 has n/p of 0.5 and is stable. It is rare on earth, but can be produced from the decay of tritium, T.

Perhaps one could clarify the teacher's comment.

Morbius
Dearly Missed
My teacher said that if an isotope has a neutron to proton ratio that is greater than 1.2 it is radio active, but he said there is one exception when the ratio is lower than 1.2 .. something about the isotope being synthetic. Can someone help me an explain exactly what this exception is.

Thank you.

Btw i originally posted this question in the chemistry section and was referred here.
dionysian,

I'm sorry but your teacher is just flat out WRONG!!!

Whether an isotope is radioactive or not is more complicated than a ratio of neutrons
to protons.

The stability of an isotope is dictated by quantum mechanics; and there are some things
that your teacher's rule doesn't take into account. For example, a nucleus is more
stable if there is a shell closure. You may be familiar with shell closures of electrons
in the periodic table of the elements - the noble or inert gases are the result of a shell
closure.

The same thing happens in the nucleus. The nucleons - protons and neutrons are in
shells. When a shell closes it gives rise to what is called a "magic number" - there
are certain numbers of protons and neutrons for which the nucleus gets additional
stability because that number of protons or neutrons exactly closes a shell.

Additionally, if you look at what is called the "Semi-Empirical Mass Formula" which
gives an approximation of the binding energy as a function of the number of protons
and neutrons:

http://en.wikipedia.org/wiki/Semi-empirical_mass_formula

The Coulomb term which represents the repulsion of the protons is an "unbinding" energy;
it is a negative term that decreases the stability of the nucleus. Note that this term
goes like Z * (Z-1) or approximately like Z squared. This means that nuclei with higher
atomic numbers have to have a greater proportion of neutrons to make up for this
"unbinding energy" that goes like Z squared. Any "rule" or "ratio" can't be independent
of Z; it has to depend on the atomic number Z of the nucleus.

Your teacher took a very complex calculation and turned it into a dependence on a simple
ratio; and I'm sorry to say your teacher is WRONG!!!

If your teacher doesn't understand the physics; then the teacher should not be proffering
explanations for something he doesn't understand.

Dr. Gregory Greenman
Physicist

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I am actualy glad to hear this, i hate this teacher.

I asked him about this today and after being yeld at for not paying attention he told me that if an isotope has a np ratio below 1 it is a positron emitter. He also said that if the amu of the isotope is lower than the amu of the element than it also radioactive... This teacher seams to not like explaining things and always seems to give me very short hurried ansewer to get me to go away.

I take that there is a lot going on here that i dont understand.
This is chem 1 and i am not sure why we are even learning this stuff right now the section that deals with nuclear chem is in the back of our book.

Anyways Thank you for the replies

and i am going to have him explain his "rule" for the case of Sc-46 which seems to contradict what he told me.

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If there's anything I learned about chemistry, it's that the professor gives you general rules that are good to follow, then you just have to memorize the exceptions to the rule.

Morbius
Dearly Missed
If there's anything I learned about chemistry, it's that the professor gives you general rules that are good to follow, then you just have to memorize the exceptions to the rule.
Candyman,

In this case, however, the teacher's rules are just plain WRONG!!!

Yes - one can have a general rule that fits a majority of the cases, and then one can
note the exceptions.

However, in this case; the general rule doesn't work - and it isn't based in the physics.

This teacher is an IDIOT!!! I'm afraid that there are too many teachers like this.

Every year I volunteer to work the "Expanding Your Horizons" conference in our area.
It's a workshop for junior and senior high school women to encourage them to pursue
careers in the sciences.

On of my Lab collegues was there with a display consisting of radiation detectors and
a whole host of items that you will find around your house that are radioactive. [ If you
have a single-lens reflex camera; Nikon, Minolta, Canon...; one of the most radioactive
things in your house is that 50mm lens on the front. Optical glass has thorium in it.]

Some of the other items in his collection are fossils. He told me he was at a Bay Area
high school showing them this stuff. One of the items was a fossilized shark's tooth.
The science teacher asked him what he did to the shark's tooth to make it radioactive.

"Nothing" was his reply, and he explained that 100 years ago when the shark was alive,
it was swimming in the saltwater of the sea, ingesting the saltwater, and its body was
extracting the minerals from the water, which go into making up the teeth. Some of those
minerals are salts of uranium and thorium.

The teacher inquired, "You say that shark's tooth is 100 years old?" "That's correct",
he replied; after which the teacher said, "Then how can it be radioactive, since Man

Somewhere in the Bay Area is a high school science teacher so STUPID and IGNORANT
of science, as to think, and be teaching that Man invented radioactivity in 1945!!

Dr. Gregory Greenman
Physicist

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Astronuc
Staff Emeritus
if an isotope has a np ratio below 1 it is a positron emitter.
This is not quite true - there are isotopes of n/p > 1, which are positron emitters. The heaviest positron emitters Tl-176 and Au-171, have n/p of 1.173 and 1.164! Note that the half-lives for the radionuclides above the stability line tend to be shorter that those below.

Looking at Cl-33, Ar-35, K-37, Ca-39, . . . and an host of other isotopes transform by electron capture (EC), and in fact, EC is more common than positron emission. So just because n/p < 1, that doesn't assure (guarantee) positron emission as the decay mode.

Here is a list of common positron emitters and the reactions used to produce them - http://www-nds.iaea.org/medical/positron_emitters.html
Note: for Sr-82, n/p = 1.158. While this page indicates that Sr-82 is a positron emitter, the Chart of Nuclides (CoN) at BNL indicates that it transforms by EC. Similarly, Zr-89 (n/p=1.225) and I-124 (n/p=1.34) are discussed as long-lived positron emitters, but the CoN has the decay mode as EC.

On the other hand, CoN from Nuclear Data Center at Japan Atomic Energy Agency, Tokai (Japan) has Zr-89 as positron (B+, B= beta) emitter. http://wwwndc.tokai-sc.jaea.go.jp/cgi-bin/nuclinfo2004?40,89 [Broken]

See - http://wwwndc.tokai-sc.jaea.go.jp/CN04/index.html [Broken]

if the amu of the isotope is lower than the amu of the element than it also radioactive..
:surprised That statement makes no sense!

Element refers to all atoms of a specific Z (which determines chemical identity or chemical behavior), and isotopes simply refers atoms of the 'same' Z but different N or A (A = Z + N), i.e. Z = number of protons and N = number of neutrons, so A = atomic mass.

One can separate atoms of different elements by 'chemical' processes, but one must use a 'physical' process to separate isotopes, e.g. diffusion, or centrifugal force (as in centrifuge), or mass spectrometry. More recently though, use of specific light frequency (from laser) has been used to separate isotopes. The process takes advantage of the 'small' change in potential energy of the atomic electrons due to the difference in nuclear mass.

This teacher seems confused or is too lazy to learn the correct information. :grumpy: Of course, this is based on the comments in this post. Are you sure you heard the teacher correctly? :uhh:

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