Nuclear forces and Radioactivity Two forces are at work inside the nucleus of an atom

Forces act in opposing directions Electrostatic repulsion: pushes protons apart Electrostatic repulsion: pushes protons apart Strong nuclear force: pulls protons together Strong nuclear force: pulls protons together Nuclear force is much shorter range: protons must be close together Nuclear force is much shorter range: protons must be close together 

Neutrons only experience the strong nuclear force Proton pair experiences both forces Proton pair experiences both forces Neutrons experience only the strong nuclear force Neutrons experience only the strong nuclear force But: neutrons alone are unstable But: neutrons alone are unstable 

Neutrons act like nuclear glue Helium nucleus contains 2 protons and 2 neutrons – increase attractive forces Helium nucleus contains 2 protons and 2 neutrons – increase attractive forces Overall nucleus is stable Overall nucleus is stable   

As nuclear size increases, electrostatic repulsion builds up There are electrostatic repulsions between protons that don’t have attractive forces There are electrostatic repulsions between protons that don’t have attractive forces More neutrons required More neutrons required      Long range repulsive force with no compensation from attraction 

Neutron to proton ratio increases with atomic number Upper limit of stability

Upper limit to nuclear stability Beyond atomic number 83, all nuclei are unstable and decay via radioactivity Beyond atomic number 83, all nuclei are unstable and decay via radioactivity Radioactive decay (Transmutation) – formation of new element Radioactive decay (Transmutation) – formation of new element Atomic number decreases Alpha particle emitted Mass number Atomic number

Beta particle emission Neutron is converted into a proton + electron Neutron is converted into a proton + electron Proton stays in nucleus Proton stays in nucleus Electron is emitted (beta particle) Electron is emitted (beta particle) 

Atomic number increases with beta emission Here atomic number actually increases, but serves to reduce the neutron:proton ratio Here atomic number actually increases, but serves to reduce the neutron:proton ratio Beta particle emission occurs with neutron-excess nuclei Beta particle emission occurs with neutron-excess nuclei Alpha particle emission occurs with proton-heavy nuclei Alpha particle emission occurs with proton-heavy nuclei Beta particle emitted

Positrons and antimatter Protons are converted to neutron and positively charged electron (positron) Protons are converted to neutron and positively charged electron (positron) Neutron stays in nucleus Neutron stays in nucleus Positron emitted Positron emitted Positron is antimatter and is annihilated by electron: Positron is antimatter and is annihilated by electron: 

Summary of nuclear processes Alpha emission: Alpha emission: Mass number and atomic number decrease Mass number and atomic number decrease Beta emission: Beta emission: Mass number same, atomic number increases Mass number same, atomic number increases Positron emission: Positron emission: Mass number same, atomic number decreases Mass number same, atomic number decreases Gamma ray emission: Gamma ray emission: Mass number and atomic number same Mass number and atomic number same

Analyzing nuclei: filling in the blanks Mass number = protons + neutrons Mass number = protons + neutrons Atomic number = protons Atomic number = protons Element identity = atomic number Element identity = atomic number

Writing nuclear equations Rules for balancing nuclear equations: Rules for balancing nuclear equations: 1. Conserve mass number (protons + neutrons) 2. Conserve atomic number (nuclear charge)

Mass number sum: Mass number sum: 234 = ? ? = 0 Atomic number sum: Atomic number sum: 90 = 91 + ? ? = -1 Particle is Particle is

Mass number sum: Mass number sum: 234 = ? + 0 ? = 234 Atomic number sum: Atomic number sum: 90 = ? - 1 ? = 91 Nucleus is Nucleus is

Worked examples

Creation of radioisotopes Isotopes are created by bombarding nuclei with smaller particles Isotopes are created by bombarding nuclei with smaller particles Neutrons Neutrons Protons Protons Alpha particles Alpha particles Other nuclei Other nuclei

Radioactive decay occurs in series of steps The decay series from uranium-238 to lead-206. Each nuclide except for the last is radioactive and undergoes nuclear decay. The left-pointing, longer arrows (red) represent alpha emissions, and the right-pointing, shorter arrows (blue) represent beta emissions.series

Half-life measures rate of decay Concentration of nuclide is halved after the same time interval regardless of the initial amount – Half-life Concentration of nuclide is halved after the same time interval regardless of the initial amount – Half-life Can range from fractions of a second to millions of years Can range from fractions of a second to millions of years

Half-life calculations 131 I decays to 131 Xe with a half-life of 8 days 131 I decays to 131 Xe with a half-life of 8 days How much remains after 40 days if there are 10 grams initially? How much remains after 40 days if there are 10 grams initially?

The Dating Game Carbon-14 is produced in the upper atmosphere by the bombardment of nitrogen atoms with neutrons: Radioactive 14 CO 2 is produced, which mixes with ordinary 12 CO 2 and is taken up by plants during photosynthesis.

Carbon Dating During an organism’s life, 14 CO 2 and 12 CO 2 are in equilibrium at a ratio of 1: When organism dies, 14 C/ 12 C ratio decreases as 14 C undergoes  decay to 14 N. Measuring 14 C/ 12 C ratio determines age of sample with high degree of certainty. Ages of 1000–20,000 years are commonly determined. The half-life for 14 C is 5730 years.

The age of the earth U-238 decays eventually to Pb-206 U-238 decays eventually to Pb-206 Since half-life of U-238 is so long (4.5 billion years), the atom of Pb-206 appears almost instantly after its decay Since half-life of U-238 is so long (4.5 billion years), the atom of Pb-206 appears almost instantly after its decay If the mineral was once pure U-238, after some billions of years it becomes a mixture of U and Pb If the mineral was once pure U-238, after some billions of years it becomes a mixture of U and Pb Measuring the ratio of Pb:U gives us the age of the rock Measuring the ratio of Pb:U gives us the age of the rock Note that the U-238 half-life is of the order of the age of the earth. If the earth was 6,000 years old or 50 billion years old it would not work Note that the U-238 half-life is of the order of the age of the earth. If the earth was 6,000 years old or 50 billion years old it would not work

Other nuclear processes: fission and fusion Attempts to grow larger nuclei by bombardment with neutrons yielded smaller atoms instead. Attempts to grow larger nuclei by bombardment with neutrons yielded smaller atoms instead. Distorting the nucleus causes the repulsive forces to overwhelm the attractive Distorting the nucleus causes the repulsive forces to overwhelm the attractive The foundation of nuclear energy and the atomic bomb The foundation of nuclear energy and the atomic bomb

Inter-changeability of mass and energy When a radioactive nucleus divides to give two smaller ones, the combined mass of them is lower When a radioactive nucleus divides to give two smaller ones, the combined mass of them is lower A  B + C M A > M B + M C Loss in mass equals energy given out Loss in mass equals energy given out E = mc 2 Tiny amount of matter produces masses of energy: Tiny amount of matter produces masses of energy: 1 gram  J In chemical process 1 gram may produce 10 3 J (10 11 less) In chemical process 1 gram may produce 10 3 J (10 11 less) Energy and mass are conserved, but can be inter-changed Energy and mass are conserved, but can be inter-changed

Nuclear fission Nuclear fission produces nuclei with lower nucleon mass Nuclear fission produces nuclei with lower nucleon mass One neutron produces three: the basis for a chain reaction – explosive potential One neutron produces three: the basis for a chain reaction – explosive potential

Chain reactions require rapid multiplication of species

Nuclear fusion Small nuclei fuse to yield larger ones – losing nucleon mass Small nuclei fuse to yield larger ones – losing nucleon mass Example is the deuterium – tritium reaction Example is the deuterium – tritium reaction High energy output High energy output Clean products – no long-lived radioactive waste or toxic heavy metals Clean products – no long-lived radioactive waste or toxic heavy metals Problem is providing enough energy to initiate the process Problem is providing enough energy to initiate the process + E+ E

Biological Effects of Radiation The penetrating power of radiation is a function of its mass:  -rays >  -particles >>  -particles. The penetrating power of radiation is a function of its mass:  -rays >  -particles >>  -particles. When ionizing radiation passes through tissue it removes an electron from water to form H 2 O + ions. When ionizing radiation passes through tissue it removes an electron from water to form H 2 O + ions. The H 2 O + ions react with another water molecule to produce H 3 O + and a highly reactive OH radical. The H 2 O + ions react with another water molecule to produce H 3 O + and a highly reactive OH radical. Free radicals generally undergo chain reactions, producing many radicals in the biomolecules. Free radicals generally undergo chain reactions, producing many radicals in the biomolecules.

Biological Effects of Radiation02  -rays are particularly harmful because they penetrate in the same way as X rays.  -rays are particularly harmful because they penetrate in the same way as X rays.  -particles interact with the skin and  -particles interact up to 1 cm into the tissue  -particles interact with the skin and  -particles interact up to 1 cm into the tissue  -particles are particularly dangerous when ingested or inhaled.  -particles are particularly dangerous when ingested or inhaled.

Different units for measuring radiation The Curie Measure of amount of radioactivity Amount of material that produces 3.7x10 10 decays per second The Roentgen (gamma and X- ray) Measure of interaction with air Amount of radiation needed to produce 2x10 10 ion pairs in air The Rad Radiation absorbed dose Dosage of radiation able to transfer 2.4x10 -3 cal to one kg of matter The Rem Measure of biological damage Determined from rem and some factor which depends on the type radiation (1 for beta and 10 for alpha)

Biological Effects of Radiation Not all forms of radiation have the same efficiency for biological damage. Not all forms of radiation have the same efficiency for biological damage. To correct, the radiation dose is multiplied by the relative biological effectiveness (RBE), which gives the roentgen equivalent for man (rem). To correct, the radiation dose is multiplied by the relative biological effectiveness (RBE), which gives the roentgen equivalent for man (rem). RBE is about 1 for  - and  - and 10 for  radiation. RBE is about 1 for  - and  - and 10 for  radiation. SI unit for effective dosage is the Sievert (1 Sv = RBE x 1 Gy = 100 rem). SI unit for effective dosage is the Sievert (1 Sv = RBE x 1 Gy = 100 rem).

Biological Effects of Radiation

Sources of radiation