Atomic nuclei?

[Reading assignment: Hobson, Chapter 14]

Why do we think there is such a thing as an atomic nucleus? Or...

How can you tell if there's a rock in that pudding??

This is an English Christmas pudding, which is nearly solid and can stand up by itself--unlike American puddings, which are more nearly liquid!

We shall see that the answer is to shoot it!

The story of the nucleus starts with the discovery of something much smaller:

Cathode rays

1869: Johann Wilhelm Hittorf -- eventually a professor at the University of Muenster--finds that if you attach electrodes to an "almost-vacuum" tube that you could generate a glow, later dubbed "cathode rays".

  • The rays were attracted to plates with a positive electric charge.
  • Seemed like the beams were made of identical particles. They all had the same mass: about 1/1000 of that of a hydrogen ion.

These are electrons.

Another cathode-ray tube

tvMany people used to own this kind of cathode ray tube.

The screen is made with "phosphors" that glow where they're hit with electrons.

To make a television image: The cathode ray (electron beam) is steered back and forth across the screen many times in each second, and switched off and on, leaving a pattern of bright and dark spots behind.

 

 

Plum pudding atomic model

So, there are electrons, which have a negative electric charge. But except for a bit of static electricity when we drag our feet on carpet, matter is pretty close to neutral.

So, where is the positive charge?

1904: J. J. Thomson put forth a plum pudding model of the atom to account for electrons: that they are lightweight lumps floating in a uniform "pudding" of positive charge.

Back to our plum pudding question

How can you tell if there's a rock in that pudding??

Geiger, Marsden, and Rutherford decided to shoot a thin foil with atomic-sized BBs...

Geiger-Marsden experiment

Rutherford had discovered that Radium gave off highly energetic 'alpha' particles. Sometimes written as the greek letter "$\alpha$". (Nowadays we know these alphas are helium nuclei).

Whenever an alpha hits a ZnS screen there is a brief flash of light.

His students Geiger and Marsden undertook to shoot a thin gold foil with alphas.

[Writing] What would you expect?

Scientists knew there were electrons in matter. Electrons are much lighter than the alpha particles. So on a scale where the alpha particles are like _tennis balls_, the much lighter electrons have a weight like _ping-pong balls_: well, actually, even lighter.

Is there anything else at the atomic scale? What's the stuff that's positively charged? A smooth "jello" of positive charge? or something denser and lumpier?

Pudding it is!


Geiger and Marsden set their ZnS screen on the far side of the gold foil (just a few atoms thick) and rarely found any alpha's that didn't go straight through: $\theta=0$.

Tennis balls vs ping pong balls - One alpha weighs more than 4000 times the weight of 1 electron, so it should blow past an electron.

=> pretty much what you'd expect for "pudding" with the positively charged mass smeared out, and only ping-pong-ish lumps.

While things are set up...

A year later, they thought, maybe they should try placing detectors further around their gold sample.

The result blew them away:

The nucleus

They occasionally found alphas coming off at very large scattering angles

It was hard to escape the conclusion that there was something very small and very heavy in there.

The atom

The nucleusA positively charged nucleus surrounded by a cloud of electrons.

Mass number = protons + neutrons

Atomic number = # of protons

Is there anything about this picture that makes you uncomfortable?

Like the fact that those protons aren't flying away from each other?

A new force

  • Stronger than the electric force.
  • Stronger than gravity.
  • Attractive between any combination of protons and neutrons.

$=>$ the strong 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.

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 (1 mole is $6 \times 10^{23}$ particles).

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 largest.
  • 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", occasionally one strays farther away.

Far enough, and the electric repulsion is stronger than the Strong attraction.

Bring mousetrap to class

$\Rightarrow$ alpha ($\alpha$) decay

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

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.

Discovery

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 amount of Uranium present in a sample--not the chemical form it was in.

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.

Radioactive decays

alpha decay: an $\alpha$ particle is the same as a $He$ nucleus. For example:

${}_{92}^{238}U \rightarrow {}_{90}^{234}Th + {}_2^4 \alpha (+ \gamma)$

Notice: that sum of the atomic numbers (proton numbers) of everything on the left is equal to the sum of the atomic numbers on the right.

Also, the sum of the mass numbers of everything on the left is equal to the sum of the mass numbers of everything on the right.

beta decay: Occasionally, a neutron spontaneously transforms into a proton + electron ("beta" particle), and the electron is kicked out of the nucleus. For example:

${}_6^{14}C \rightarrow {}_7^{14}N + {}_{-1}^0\beta (+\gamma)$

The nucleus left behind is called the daughter nucleus, e.g. ${}_{90}^{234}Th$ and ${}_7^{14}N$ in these reactions.

[Writing]

${}_{92}^{238}U \rightarrow {}_{90}^{234}Th + {}_2^4 \alpha$

${}_6^{14}C\rightarrow {}_7^{14}N + {}_{-1}^0 \beta$

Write down the decays below in the same form as above. Figure out the daughter nucleus atomic number and mass number, then use the periodic table (back of your book) to figure out what element the daughter nucleus is.

  1. ${}_{38}^{90}Sr$ emits a ${}_{-1}^0\beta$ particle.
  2. ${}_{84}^{214}Po$ emits an ${}_2^4\alpha$ particle.
  3. ${}_{86}^{222}Rn$ emits an ${}_2^4\alpha$ particle.

Suggested exercises

Chapter 14, Conceptual Exercises: 1, 2, 3, 7, 9, 10, 14,