_________ are radioactive isotopes, they are used, not only, in the curing of diseases, but in the preservation of ______, the tracing of _______ in reactions, and to power the equipment in ________
Radioactive ______ are isotopes that are used to track how substances change and move. For example, a sample of sugar can be labeled with ________; that is some _______ atoms in sugar molecules are replaced by _______ atoms that can be detected by _______ counters.
- radiation counters
When sugar molecules are labeled with ________, the progress of even minuscule amounts, too small to be detected by other means, can be monitored.
In biology, radioisotopes are used to trace _______ _____, in chemistry, they are used to trace ______ mechanisms, and in geology, they are used to trace the age of _____
- metabolic pathways
The energy released when the nucleons in a nucleus adopt a more stable arrangement can be calculated by comparing the masses of the ______ ______ and the _______ _______.
- nuclear reactants
- nuclear products
Einstein's theory of relativity tells us that the mass of an object is a measure of its energy content. Therefore, the greater the mass of an object, the ______ its energy. State the equation that relates this.
- E(energy) = m(mass) * c2(speed of light)2
It follows from the theory of relativity, that loss of energy is always accompanied by loss of _____. That loss is usually too small to detect, even in strongly ________ chemical reactions.
The nuclear binding energy, Ebind, is the energy ______ when protons and neutrons come together to form _______. All binding energies are _______, meaning a nucleus has a ______ energy than its constituent nucleons. So the greater the binding energy, the _______ the energy of the nuclide.
Binding energy is usually reported as the energy per nucleon, but another way to think of it is as the ______ ______ that must be supplied to separate a _____ from a ______.
- average energy
Einstein's equation can be used to calculate the ______ ______ ______ from the difference in mass, Δm, between the _______ and the separated _______. State an equation for both Δm & Ebind(nuclear binding energy)
- nuclear binding energy
- Δm = [Σm(products) - Σm(reactants)]*mu
- Ebind = |Δm| * c2
Binding energies are reported in ______ or ______. State the relevant conversions, **hint: one of the conversions is into joules
electronvolts or megaelectronvolts
- 1MeV = 106 ev
- 1ev = 1.60218 * 10-19J
Because the masses of nuclides are so small, they are normally reported as a multiple of the _____ _____ _____, mu. It is defined exactly as ___th the mass of one atom of carbon-12. State the formula
- atomic mass constant (mu)
- mu = [m(12C)/12]
When calculating |Δm| for a nuclear reaction, the mass of an atom of 1H is used in place of the mass of each ______. This strategy allows us to use readily available ______ masses instead of the masses of bare atomic nuclei to calculate |Δm|, because the number of electrons in the ______ will be the same as the number of electrons in the ___ atoms on the other side of the equation and the masses of the electrons will ______.
The contribution to the total mass that is due to the _______-______ binding energy is only about mu/106 per proton, and so it can be ________ in elementary calculations.
State a unit using kilograms that is equivalent to one joule
1kg*m2s-2 = 1J
If you see "number of disintegrations" in a question, think number of ________ ______
If you are asked to find the age of a sample and are given: N, N0, and a decay constant (k), which formula would you use, and what would you manipulate it to look like
Formula: N = N0 * e-kt
Derived formula: t = -t/k * ln(N/N0)
If you are asked to find the age of a sample and are given: N, N0, and its half-life (t1/2), which formulas would you use, and what would you manipulate it to look like? This is true because the value _____ and ____ are equivalent.
Formulas: t = -t/k * ln(N/N0) & t1/2 = ln2/k
Derived formula: t = -(t1/2/ln2) * ln(N/N0)
-(1/k) and -(t1/2/ln2) are equivalent
When asked to work with disintegration of a sample that is of a mass not equal to 1g what must you do? What will your units be when it is done?
Account for the specified mass by dividing the number of disintegrations by the stated mass and then dividing by the time state. For example 600dis*g-1h-1
Which formula do you use for calculating the binding energies as opposed to calculating binding energies specifically for fission reactions?
Binding energy formula: E = |Δm|*c2
Fission reaction binding energy formula: ΔE = NΔmc2 (Where N is the number of atoms)
In a fission reaction, how would solve for N (number of atoms)
N = mass of sample/ mass of atom
To construct an overall rate law from a mechanism, we write the rate law for each the _______ reactions that have been proposed, then ________ them into an overall rate law. One procedure is to use the ______ ______ _______.
- steady state approximation
If the answer is requested in J*nucleon-1, what do you do after you get the answer in J?
Divide by the mass superscript on the element
If you are told to find the energy released per gram of starting material, we first convert mu from ______ to _____. Then we divide ΔE by _____ and multiply 1/mu in ____