Definitions

Nucleons: Subatomic particles in the nucleus : protons and neutrons
Radionucleotides: Radioactive nuclei. Unstable nuclei that spontaneously emit particles and electromagnetic radiation.
Radioisotopes: Atoms containing radioactive nuclei.

Types of Radioactive Decay

When unstable nuclei decay, the reactions they undergo generally involve one or more of the following particles listed in the first column. Some facts about these particles may be found in the next 5 columns. In the 7th column you will find an example of each type of decay. Notice that for an alpha particle decay, the equation is balanced with regard to atomic number (92, 90+2) and atomic weight (238, 234+4). This type of balancing is true for all nuclear reactions. In the last column are instructions for how to predict when each type of emission or capture will occur. Fore example, if the atomic number is greater than 83, alpha particle decay is most likely.

particle	What is it?	symbol	charge	mass	relative penetrating power	Example	Applies to which particles
alpha particles	helium nuclei	2He4 or 2a4	+2	6.664 E-24 g	1	92U238 => 90Th234 + 2He4	Atomic Numbers > 83; the 2 p+ 2n0 loss brings the atom diagonally back to the belt of stability.
beta particles	high speed electrons	-1eo or -1Bo	-1	9.11 E-28 g	100	53I131 => 54Xe131 + -1eo	Isotopes below the belt of stability (high neutron : proton ratios). Causes a loss of 1 neutron and a gain of 1 proton.
	When a B-particle is emitted, the at. no. increases by 1. A neutron is converted into a p+ and e-:     on1 => 1p1 +  -1eo
gamma Rays	high energy photons	ogo	0	0	10000
	Generally accompanies other radioactive radiation because it is the energy lost from other nucleon changes. Gamma radiation is generally not shown in the nuclear equation.
positron emission	positron	1eo	+1	9.11 E-28 g		6C11 => 5B11 + 1eo	Isotopes above the belt of stability (low neutron : proton ratios). Causes a loss of 1 proton and a gain of 1 neutron.
	Causes the atomic number to decrease. It converts a proton to a neutron + positron 1p1 => on1+ 1eo
electron capture	inner shell electron	-1eo	-1	9.11 E-28 g		37Rb81+ -1eo=> 36Kr81	Isotopes above the belt of stability (low neutron : proton ratios). Causes a loss of 1 proton and a gain of 1 neutron.
	The nucleus capture an inner shell electron; thereby converting a p+ to a no 1p1 + -1eo => on1

:Stable n:p ratios:

Neutrons are needed to hold protons together in the nucleus by the strong force. At low atomic numbers, the ratio of neutrons to protons in stable isotopes is generally very close to 1. As the atomic number rises, so does the neutron/proton ratio, such that at atomic number 80, stable isotopes have a ratio of about 1.5. This information is tabulated below.

atomic number	7	40	50	80
ratio n/p for stable isotopes	1	1.25	1.4	1.5

Problem	Predict the type of decay of the isotope 92U238
	explanation	emission	preliminary equation	balancing to solve for X
Solution	z > 83	alpha	92U238 => X + 2He4	92U238 => 90Th234 + 2He4

For several more problems like this one, take the following link: radioactive emission worksheet: You should practice these and then return to continue.

Radioactive Series: Using the above rules, one can follow the decay of U²³⁸ to Pb²⁰⁶ although I would not have expected the 2^nd and 3^rd emissions.
These are presented to you as a matter of interest. You will not be expected to learn or reproduce these equations.

Z > 83 so  alpha particle emission	92U 238 => 90Th234 + 2He4
unpredicted Beta particle emission	90Th234 =>  91Pa234 + -1eo
unexpected Beta particle emission	91Pa234 =>  92U234 + -1eo
Z > 83 so alpha particle emission	92U234 => 90Th230 + 2He4
Z > 83 so  alpha particle emission	90Th230 => 88Ra226 + 2He4
Z > 83 so  alpha particle emission	88Ra226 => 86Rn222 + 2He4
Z > 83 so  alpha particle emission	86Rn222 => 84Po218 + 2He4
Z > 83 so  alpha particle emission	84Po218 => 82Pb214 + 2He4
132/82 = 1.61 high so Beta particle emission	82Pb214 => 83Bi214 + -1eo
131/83 = 1.59 high so Beta particle emission	83Bi214 => 84Po214 + -1eo
Z > 83 so  alpha particle emission	84Po214 => 82Pb210 + 2He4
128/82 = 1.57 high so Beta particle emission	82Pb210 => 83Bi210 + -1eo
127/83 = 1.53 high so Beta particle emission	83Po210 => 84Po210 + -1eo
Z > 83 so  alpha particle emission	84Po210 => 82Pb206 + 2He4
124/82 = 1.51 no further emission

Stable nuclear configurations:

Some configurations of protons and neutrons are particularly stable just as some configurations of electrons (2, 10, 18, 36, 54, 86) are.
proton numbers: 2, 8, 20, 28, 50, 82
neutron number: 2, 8, 20, 28, 50, 82, 126
nuclei with even numbers of protons and neutrons are more stable than those with odd numbers.

Nuclear Transmutations: occur when nuclei are struck by neutrons or other nuclei. These reactions are useful in creating new radioisotopes.

Notation: The reaction in which N-14 is bombarded with an alpha particle:  ₇N¹⁴ + ₂He⁴ => ₈O¹⁷ + ₁H¹ is written as
₇N¹⁴ (a, p) ₈O¹⁷ in the following order: target nucleus, (bombarding particle, ejected particle), product nucleus.
Go to a worksheet on using nuclear transmutation notation

Rates: Half life is the time required for half of the radioisotope to react.

Dating: Carbon-14 has been used to determine the age of organic materials.

In the upper atmosphere, ₇N¹⁴ captures a neutron to form ₆C¹⁴
₇N¹⁴ + ₀n¹ =>  ₆C¹⁴ + ₁p¹ which supplies a constant source of C-14.
However ₆C¹⁴ is radioactive and decays back to ₇N¹⁴ with a half life of 5730 years.   ₆C¹⁴ =>  ₇N¹⁴ + _-1e^o

We assume that the ratio of C-14 to C-12 in the atmosphere has been constant for at least 50000 years. So long as an organism is living, the  CO₂cycle keeps renewing the supply of C-14 keeping the ratio of C-14 to C-12 constant. Upon death, the organism does not replenish its supply of C-14 while existing C-14 decomposes with a half life of 5730 years. The smaller the fraction of C-14 in the organism, the longer ago that organism died. For example, if the organism has half the amount of C-14 that is present in the atmosphere, the organism probably died 5730 years ago.

Mass Defect:

It is experimentally observed that the mass of an atom (containing neutrons) is always slightly less than the sum of the masses of its component particles. The difference between the atomic mass and the sum of the masses of its protons, neutrons, and electrons is called the mass defect.

isotope		Should weigh:	Do weigh:	Mass Defect:
Hydrogen	1.0073 + .00055 =	1.00785	1.0078	none
Deuterium	1.0073 + .00055 + 1.0087 =	2.01655	2.0140	.0025
Tritium	1.0073 + .00055 + 2(1.0087) =	3.02525	3.01605	.0092

The loss in mass is accounted for by Einstein’s E = mc², which describes conversions between matter (m) and energy (E). When the nucleus is being formed, some matter was converted into energy (called nuclear binding energy). Problems in calculating mass defect and Problems calculating energies associated with mass defects

Energy changes in nuclear reactions

Given the nuclear reaction: ₉₂U²³⁸ => ₉₀Th²³⁴ + ₂He⁴ , and given the masses of the three atoms (238.0003 amu, 233.9942 amu, 4.0015 amu) calculate the mass and energy change per mole associated with this reaction.

[Energy - mass conversion equation: E = m c² ;  Energy conversion formula: 1.00 J = 1.00 kg m² / s² ]

mass change	mass of products – mass of reactants = 233.9942g + 4.0015g – 238.0003g = -.0046 g (exothermic)
energy change	.0046g * [3.00 E8 m/s]2 [1kg/1000g] = -4.1 E11 kg m2/s2 = -4.1 E11 J

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