One Chapter 10

CHAPTER 10

Investigating the Nucleus

• The model of the atom built up over time includes the following information about the nucleus:
  • It has a positive charge.
  • The diameter of the nucleus is about 10^-14 m
  • It takes up only a tiny part of the atom’s total volume.
  • The nucleus contains nearly all of the mass of the atom.
• Questions remained regarding the nucleus
  • What is the internal structure of the nucleus?
  • Is it one large mass or a number of particles?
  • How can its properties be investigated?
• The questions scientists had about the origin of alpha and beta particles led scientists to investigate radioactive decay.
• This study led to an understanding of the structure of the nucleus.

Isotopes

• Elements in our periodic table are arranged by atomic number.
• In Mendeleev’s table, they were arranged by atomic mass (This had problems of reversals).
• Rutherford suggested that most of the mass of an atom is concentrated in the nucleus.
• Bohr suggested the existence of allowed orbits for the electron (electron shells).
• Electrons could not exist between allowed orbits.
• Each orbit had a specific energy for the electron.
• Electrons will always move into electron shells with the least amount of energy.
• Electron shells are named K, L, M, N, O, P, etc.
• Each atom of an element has the same number of protons but the number of neutrons may vary.
• Isotopes – Atoms of a substance that have different numbers of neutrons. They have the same atomic number but different atomic masses.
• Most elements have several isotopes that vary in amount present in nature.
• The atomic mass in the periodic table is an average for all isotopes.
• Atomic mass in the periodic table takes into account the relative abundance of different isotopes.
• Atomic mass in the periodic table takes into account, the relative abundance of different isotope.

NATURAL TRANSMUTATIONS

• Scientists working with radioactive elements noted that helium was usually present.
• This led Rutherford to propose that the alpha particle was a helium atom.
• Rutherford carried out an experiment which proved his hypothesis.

• Alpha particles from radioactive radon passed through the thin walled glass container and were trapped in the thick walled outer chamber.
• More mercury is put into the outer chamber to concentrate the alpha particles.
• A discharge across electrodes and spectral analysis revealed a helium spectrum.
• Spectral analysis of the radon left after decay showed that polonium had been produced in the decay of the radon.
• Transmutation - The process of changing one element into another.
• Alpha decay - Transmutation that occurs by the emission of alpha particles (a).
• Beta decay - Transmutation that occurs by the emission of a beta particle (b).
• Decay - An atom of large mass is transmuted into an atom of smaller mass.

Alpha Decay

• Alpha decay results in the emission of an alpha particle.
• The alpha particle is given the following symbol when used in formulas.

• The general equation for alpha decay is:

BETA DECAY

• During beta decay
  • Atomic number increases by one
  • Atomic mass remains the same.
• Beta particles are electrons with high speed
• Beta particles are given the symbol.

• In the symbol, (-1) tells us charge is -1 and 0 tells us that the mass is negligible.
• The emission process involves a neutron breaking up into a proton and an electron.
• The general equation for beta decay is.

GAMMA RADIATION

• Usually accompanied by alpha and beta decay.
• Consists of a photon with no mass or charge.
• Results in no change in atomic mass or atomic number.
• The symbol used for gamma radiation is:

• The general equation for gamma decay is:

• Alpha and Beta decay is illustrated by the uranium to lead decay series.

DECAY RATE AND HALF LIFE

• Radioisotopes - radioactive isotopes.
  • disintegrate spontaneously
  • rate of disintegration depends only on the specific element that is disintegrating.
• Half-life - The time required for one-half of the atoms in any sample of a radioisotope to decay.

e.g. Thorium-234 has a half life of 24 d

If we start with 1 kg, then in 24 days, there is 0.5 kg left. There

will be 0.25 kg left in 48 days, and 0.125 kg in 72 days.

• Generally:

• In the formula, n = the number of half lives, N_o = amount started with, and N = the amount left after n half lives.

e.g. The half-life of Strontium-90 is 28 a. If 60 g are currently in a

sample of soil, estimate the amount 90 a later.

n = 3.214

N_o = 60 g

N = ?

N = 60 g(1/2)^3.214

N = 6.5 g

• With this equation, given the half-life of a radioisotope, and the original amount of the isotope present, the age of the sample can be determined. There are important applications in archaeology and geology.
• Half-life is different for each different radioactive element.
• e.g. radon-226 has a half life of 4 d
• polonium-214 has a half life of 1.64 X 10^-4 s
• Uranium-238 has a half life of 4.5 X 10⁹ a
• Radioactivity can be measured with a Geiger counter. The unit used is the Becquerel (Bq).
• 1 Bq = 1 decay per second
• 1 Bq = 1 emission per second
• The level of emissions is proportional to the mass of the sample.

e.g. A 1 kg sample of thorium has 2 times the radioactivity as 0.5 kg.

Radioactive Dating

• Carbon has two isotopes. They are carbon-12 and carbon-14. Carbon-14 is radioactive but carbon-12 is not.
• Carbon-14 is created in the upper atmosphere by collisions between high energy particles from the sun and air molecules.
  • Nitrogen is changed to carbon-14
  • Carbon-14 combines with oxygen to produce carbon dioxide gas.
  • Plants take in the carbon dioxide and eventually all living things have some carbon-14 in them.
  • The amount of carbon-14 in a living organism is fairly constant.
  • Once the organism dies, the amount of carbon-14 decreases because it decays but no new carbon-14 replaces it.
  • It is the emission difference between living and non-living that determines age.
  • Carbon-14 has a half-life or 5730 plus or minus 30 years.
  • e.g. A living tree produces radioactivity of 0.30 Bq when a 1 g sample is used.
  • A 1 g sample of a dead tree gives a reading of 0.075 Bq. This is a
  • carbon-14 test. How old is the dead tree?
  • n = ?
  • N_o = 0.30 Bq
  • N = 0.075 Bq

0.75 = 1(1/2)ⁿ

n = 0.415

T = (T_1/2)n

T = (4.6 X 10⁹)(0.415)

T = 1.91 X 10⁹ a

• Using this technique, the age of rocks and the age of the earth can be estimated.

January 22, 2014