Topic 7.1 Extended D – Nuclear Structure and Nuclear Force

1. Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force Almost everything we observe in the world around us is sensed by the electromagnetic and the gravitational forces. Your seeing an object is because of the interaction between photons at the electrons orbiting atoms. Your feeling an object is because of the interaction between the electrons in your atoms responding to the electrons in the object you are feeling. Of course, weight is the other factor you can sense in an object. There are four fundamental forces in the universe. You have studied two of them in detail - namely the gravitational force (last year) and the electromagnetic force (this year). The next slide shows the relative magnitudes of the four forces of nature:

2. + + FYI: In this chapter and the next, we will be studying the strong and the weak forces, completing our overview of all the fundamental forces of nature. Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force ELECTRO-WEAK ELECTROMAGNETIC STRONG WEAK GRAVITY nuclear force light, heat and charge radioactivity freefall STRONGEST WEAKEST Range: Short Range:  Range: Extremely Short Range:  Force Carrier: Gluon Force Carrier: Graviton Force Carrier: Photon

3.    FYI: An alpha particle () is a double-positively charged particle emitted by radioactive materials such as uranium. Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force We studied the electrons surrounding the nucleus by observing the spectra. But how do we study the nucleus? In 1897 British physicist J.J. Thomson discovered the electron, and went on to propose a "plum pudding" model of the atom in which all of the electrons were embedded in a spherical positive charge the size of the atom: In 1911 British physicist Ernest Rutherford conducted experiments on the structure of the atom by sending alpha particles through gold leaf. If the atomic structure was as Thomson said, a beam of  particles should barely be deflected as it passed through the atom. scintillation screen Rutherford's experimental results were quite different, as the next slide will show:

4. Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force Here we see that the deflections are much more scattered... The nucleus Rutherford proposed that the positive charge of the atom was located in the center, and he coined the term nucleus. The atom "On consideration, I realized that this scattering backward must be the result of a single collision, and when I made the calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus."

5. 0 Minimum Radius of a Nucleus FYI: By using known values for both mass and speed of the  particle, and the atomic number of the atom used in the experiment, it was found that the radius of the nucleus was of the order of 10-12 m! Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force FYI: This, by the way, is an upper limit on the size. Why? In fact, if we look at a head-on collision between an alpha particle and a nucleus, we can obtain a rough value for the diameter of a nucleus. The charge of the alpha particle is 2e, and the charge of the nucleus is Ze, where Z is the atomic number of the element. The alpha particle feels a coulomb potential caused by the nucleus given by kQ r kZe r = V = If the  particle approaches from infinity, the work required to stop it so that it reverses is given by 2ekZe rmin 2kZe2 rmin = W = qV = = 2eV where rmin is the closest approach of the  particle to the nucleus. From the work-kinetic energy theorem, W = K = K - K0 mv2 2 2kZe2 rmin so that = or 4kZe2 mv2 rmin =

6. Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force All right. Suppose we have two protons in a nucleus. Then we have a huge problem. What is it? Estimate the force between two protons in a helium atom. The two positive charges feel the coulomb force: 9109(1.6 10-19)2 (110-12)2 kQq r2 = 0.00023 N = F = The two positive charges will want to accelerate apart with an acceleration of F m 0.00023 1.6710-27 = 1.381023 ms-2 = a = Since most atoms do not spontaneously disintegrate we can postulate that there must be a very strong attractive nuclear force which is able to counter the repulsive electric force. Since even in crystals (in which nuclei are very close together) the nuclei of the nearby atoms are not attracted to each other, the nuclear force must be very short ranged.

7. FYI: Thus there are isotopesof hydrogen, all having the same (+1) nucleus, but different numbers of neutrons. A neutron is slightly more massive then a proton. In fact, we can compare the masses of the electron, proton, and neutron: Mass of proton = 1840 electron masses Mass of neutron = 1841 electron masses Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force So what, exactly, is a nucleus comprised of? Perhaps you recall the instrument called the mass spectrometer. FYI: Hydrogen has three common isotopes: Hydrogen has one proton and no neutrons in the nucleus. Deuterium has one proton and one neutron. Tritium has one proton and two neutrons. All forms have a single electron. An element is ionized, and accelerated by an applied voltage in the chamber S. It is then projected into a known perpen-dicular magnetic field. Through use of such an instrument, scientists discovered different masses for hydrogen nuclei, and postulated the existence of the neutrally-charged neutron. The radius is detected, and the mass calculated: rqB v mv qB m = r =

8. FYI: A = Z + N, so that nuclear reactions do not generally include the N values (since it can be calculated). FYI: Since periodic tables are readily available, we can even get away with just showing the A number. Topic 7.1 ExtendedD –Nuclear Structure and Nuclear Force An element's characteristics are determined by the number of electrons it has (chemistry). FYI: Tritium is unstable. But deuterium is stable enough to form heavy water D2O. Note the use of the D for the special isotope symbol. The number of electrons is determined by the number of protons (opposites attract). FYI: A particular isotope of an element is called a SPECIES or a NUCLIDE. Thus we have three species, or nuclides, of hydrogen. Therefore it follows that isotopes of an element behave chemically the same. FYI: There are 6 nuclides of carbon: 11C 12C 13C 14C 15C 16C For the higher elements, we don't have special names like we do for hydrogen. We name these isotopes like this: carbon-12, carbon-14, etc. Only carbon-12 and carbon-13 are stable. In chemistry, you need only a chemical symbol, such as H, to represent hydrogen. In nuclear physics, you need to distinguish the isotopes. NUCLEAR PHYSICS CHEMISTRY H H Mass Number = A N = Neutrons Protons = Z H H H 2 1 3 1 1 1 0 1 2 deuterium hydrogen tritium