Radioactivity and the nucleus

The atom

The nucleus Nowadays, we believe that

  • Matter is made of atoms.
  • Atoms are made of electrons, neutrons and protons.
  • The neutrons and protons are together in the nucleus. And the electrons roam around through a much larger volume (the 'gray cloud' in the diagram above) around the nucleus.
  • Protons have positive charge and electrons have exactly the same amount of charge as protons, but it's the opposite (negative) charge). Neutrons have no charge.
  • A "neutral atom" has just as many electrons as protons, and so its total charge is 0.
  • Neutrons and protons weigh about the same amount. But they weigh about 1800 times as much as an electron.
  • Neutrons and protons are found together in the nucleus of an atom which makes up about 1/1,000,000,000,000,000 of the volume of an atom, but almost all of the mass of an atom. Therefore, outside of the nucleus, the atom is pretty "empty" with a small number of relatively lightweight electrons zipping around.

Since one neutron and one proton weigh almost exactly the same, the weight of of a nucleus is proportional to the total number of nucleons (both protons and neutrons are "nucleons"):

Mass number = protons + neutrons

Atomic number = # of protons

The atomic number determines how many electrons there are in a neutral atom, and that in turn determines how the atom will behave chemically.

Is there anything about this picture that makes you uncomfortable?

Does anyone know what happens when two objects, each with a positive electric charge, are placed close to each other?

A new force

The nucleus

  • Protons and neutrons are attracted to other protons and neutrons.
  • Stronger than the electric force.
  • Stronger than gravity.

$=>$ the strong force is the imaginative name given to this new force.

Isotopes

Isotopes are atoms with the same number of protons, but different numbers of neutrons.

We indicate which isotope is under discussion by writing something like

${}_6^{13}$C

  • The bottom number is how many protons the isotope has ("atomic number"). Every carbon nucleus has 6 protons.
  • The number of protons dictates how many electrons (6) it has. The number of electrons determines how an atom will interact chemically with other atoms. That's what makes it "carbon"-y.
  • The top number is the number of protons + neutrons the nucleus has ("mass number"). Since you know this one has 6 protons, this isotope must have 7 neutrons, because 6+7=13.
  • Every atom in the universe is also an isotope.

Atoms of carbon have been found with nuclei with 6, 7, or 8 neutrons. But never with 9 or more. And never with 5 or less. So, we say, "the 3 isotopes of Carbon are":

${}_6^{12}$C, ${}_6^{13}$C, and ${}_6^{14}$C.

...and we can talk about different isotopes by including their mass numbers, as in "Carbon 12" or "Carbon 13" or "C 14".

Atomic weights

If *all* males weighed 200 lbs, and *all* females weighed 100 lbs, What would you say is the "average weight of a human"?

  1. 100 lbs.
  2. 150 lbs.
  3. 200 lbs.
  4. 300 lbs.

Neutrons and protons each weigh about the same amount: 1 gram for each mole of protons, and 1 gram for each mole of neutrons.

On the periodic table, you will see the average weight--in grams / mole--of each element. You can *kind of* tell from the periodic table which isotope is the most common.

  • Which isotope of carbon's is the most common?
  • About how many neutrons does a typical boron nucleus have?

Greek "isos"=same, "topos"=place.

If you're so strong...

If this new force is so strong, why don't *all* the protons and neutrons in the world universe stick together?

In fact, every nucleus with an atomic number greater than 83 is unstable (that is, radioactive) -- ${}_{83}^{209}$Bi is the heaviest stable (not radioactive) nucleus.
  • Let "r" be the distance between two particles in the nucleus.
  • $F_\text{strong}\propto e^{-kr}$.
  • $F_\text{electric}\propto \frac{1}{r^2}$.
  • Strong Force > Elect Force
    at small distances, but

    Elect F > Strong F
    at greater distances.

    The strong force is short-range.

Radioactive decay


As the nucleons "jostle" around, occasionally one chunk strays farther away.

As one chunk gets far enough away, all of a sudden the electric repulsion is stronger than the Strong attraction, and the chunk gets violently kicked away from the nucleus.

Bring mousetrap to class

There is a flash of light in the gamma region of the E-M spectrum.

Let's say that you start with a nucleus (in the first picture) consisting of 92 protons and 146 neutrons.

  1. What element has 92 protons (has an 'atomic number' of 92)?
  2. What is the mass number of this nucleus?: Add up the # of protons + # of neutrons.
  3. Now, the nucleus loses the "chunk" of matter, consisting of 2 protons and 2 neutrons. This is a nucleus of what element?
  4. How many protons and how many neutrons are left behind after the chunk is expelled?
  5. So, the nucleus left behind is what kind of element?
  6. What is the "mass number" of the left behind nucleus?












We can write what just happened as a nuclear reaction equation: $${}_{92}^{238}U \rightarrow {}_{90}^{234}Th + {}_2^4 He.$$

You can see that both the mass numbers (top numbers) and the atomic numbers (bottom numbers = # of protons) are conserved on both sides of the arrow.

The kinetic energy released is eventually shared around as heat.

The ${}^4_2He$ "chunk" is very commonly expelled from nuclei. Before its charge was known, it was called an $\alpha$ (alpha) particle. And the reaction above is now called "alpha decay".

Some other kinds of 'chunks'

beta decay

Occasionally, a neutron spontaneously transforms into a proton + electron, and the electron is kicked out of the nucleus.

The mass of an electron is ~1/1800 of a proton. So its mass number is practically zero, but it has a charge of -1$e$. So we write an electron as... $$\beta^- = {}_{-1}^0 \beta=e^-.$$

So, we can write a nuclear reaction like this one... $${}_6^{14}C \rightarrow {}_7^{14}N + {}_{-1}^0\beta$$ in which

  • the mass numbers on the left and the right are equal, and
  • the total atomic (charge) numbers on the left and the right are equal.

There is a second kind of decay in which a proton inside the nucleus transforms into a neutron and gives off a positron: a particle with the same weight as the electron, but with a charge of +$e$. For example: $${}_6^{11}C \to {}_5^{11}B+{}_{1}^0\beta.$$

Both electron and positron emission are called beta decay.

The nucleus left behind is called the daughter nucleus, e.g. ${}_{90}^{234}Th$ and ${}_5^{11}B$ in the reactions above.

Gamma emmission

Gamma radiation is a high-energy photon--a bundle or quantum of light (electromagnetic radiation). Such a burst acts as an uncharged particle of zero mass. So, we could write a gamma (using the greek letter $\gamma$) as: $$\gamma = {}_0^0\gamma.$$ And you can see that emission of a gamma photon, while it carries away energy, does not change the mass number or the atomic number of a nucleus. Generally gammas accompany $\beta$ and $\alpha$ decay. So, the first alpha decay above should actually be written as: $${}_{92}^{238}U \rightarrow {}_{90}^{234}Th + {}_2^4 \alpha + \gamma.$$ If the alpha or beta particle is readily absorbed, you might only measure the gamma emmission with a radiation detector.

Or, the nucleus can also give off a gamma when it goes from an "excited" state, to a less excited state, without giving off any beta or alpha particles.

Ionizing radiation

The things we've looked at so far:

  • alpha particles
  • electrons (and positrons)
  • gamma rays

...all interact strongly with electrically charged objects, such as the electrons involved in chemical bonds.

So these kinds of particles are collectively called ionizing radiation: They can break chemical bonds (leaving, often, two "ions" behind).

Other nuclear emissions

There are two other particles which are spontaneously emitted from nuclei, but which our equipment can't readily detect. Both are electrically neutral. So, even though they have a lot of kinetic energy, they don't break chemical bonds.

  • The neutron is the other nucleon beside the proton: $${}_0^1n$$ While it doesn't interact with electrons or chemical bonds, it *does* interact with other nucleons. If a neutron runs into a ${}^{235}U$ nucleus it might cause the nucleus to split in two, and give off a couple of *more* neutrons. If there are lots of other ${}^{235}U$ nuclei around, this could be the beginning of a chain reaction.
  • The neutrino is a very lightweight, neutral particle. One kind is an electron neutrino, $\nu_e$. I will not keep track of neutrinos.

The striking thing is that, even with all the neutrons and protons in nuclei (particularly large ones), the number of different kinds of particles spontaneously emitted by nuclei is very small.

Discovery of radiation

1896: Henri Becquerel leaves uranium in a drawer with an unexposed photographic plate.

Shortly, Marie Curie was able to show that radioactivity depended only on the total amount of Uranium present in a sample--but not the chemical form it was in. (E.g. both uranium oxide and uranium hexafluoride are radioactive.)

She discovered radium and polonium, gave "radioactivity" its name, spent the war years promoting mobile x-ray vehicles to treat solders, became the first female professor at the Sorbonne, and earned two Nobel prizes: one each in physics and chemistry.