Nucleons and the nucleus He atom nucleus: 2p, 2n Both protons and neutrons are nucleons. Both have spin s=1/2 proton : +e charge, radius 0.9 fm neutron: 0 net charge, radius 2 fm (but it has a + inner core, - outer shell

How much do the nucleons act like balls stuck together? Zero point energy, momentum velocity: Two conclusions: nucleons are moving very fast (relativistic speeds), and something very strong is holding them together!

Once out of the nucleus, n, p aren’t much attracted to it. The new “strong” force Attractive   Same strength between n,n n,p, p,p Very short range (a few femtometers) Once out of the nucleus, n, p aren’t much attracted to it.

Nuclei and their labels Z = the number of protons in the nucleus N = the number of neutrons A = N+Z the total number of nucleons, “mass number” Proton number (Z) determines the chemical (elemental) name of nucleus: eg Z = 8 is always oxygen, no matter what N is! A = N + Z

How many neutrons are in , ?

Atomic mass unit u: One twelfth of atom mass

Stable vs unstable nuclei Why is N>Z favored energetically? p-p repulsion

P1. Which system has the highest total energy? nucleons close together in a nucleus nucleons well separated in space.

P2. Which system has the highest total mass? nucleons close together in a nucleus nucleons well separated in space.

Binding Energy Nuclear binding energy is the energy required to separate all the nucleons. We find it easily from mass differences.

Binding energy per nucleon

Fission

Nuclear emission

Called alpha, beta, gamma …in order of how easy they are to stop, if given the same energy We now know what these particles are!

Alpha Decay

Beta Decay Emission of either electron or positron a neutron can turn into a proton and vice-versa! …plus a long-mysterious particle called a neutrino, and an electron or positron

Gamma emission Nucleus just loses energy to a less excited state.

P3. In the following decay, what other particle must have been emitted P3. In the following decay, what other particle must have been emitted? A. alpha B. electron C. positron D. gamma P4. In the following fission reaction, nucleus X has which Z? A. 54 B. 144 C. 172 D. 198 P5. If a nucleus decays by positron emission a) Z increases b) Z decreases c) Z stays the same, but N increases d) Z stays the same, but A increases

Nuclear decay rates Nuclei decay randomly, a certain fraction per time period. The decay constant l is that fraction. Decay rate R or activity, (nuclei/time) is If the decay constant for an unstable nucleus is 0.03/sec, how many decays per second will occur from a sample with 1000 unstable nuclei?

Rate is proportional to number left: exponential decay

The half-life of 131I is 8. 0 days The half-life of 131I is 8.0 days. Calculate the decay constant (decays/sec) for this isotope. If there are 3 million 131I nuclei, how many decays/sec are there ? P6. What fraction of the 131I nuclei are left after a time of 32 days? A. none B. ½ C. ¼ D. 1/8 E. 1/16