CHEM 1412 Concept Review: Radioactivity & Nuclear Chemistry

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Radioisotope:  An isotope that is unstable enough to manifest radioactivity, which means that it will undergo spontaneous nuclear decay over time.

 

Common forms of Radioactive Decay

Alpha Decay: Radioactive decay that releases a high energy helium nucleus referred to as an “alpha particle.”

General formula for Alpha Decay:  $^x_yA\:\longrightarrow\:^{x-4}_{y-2}B\:+\:^4_2\alpha$

Beta Decay:  Radioactive decay that releases a high energy electron referred to as a “beta particle.”

General formula for Beta Decay:  $^x_yA\:\longrightarrow\:^x_{y-2}B\:+\:^{\:\:0}_{-1}\beta$

 

Gamma Decay:  Radioactive decay that often accompanies other radioactive decays which occurs as a result of an unstable high energy nucleus (sometimes referred to as a metastable nucleus) collapsing into a more stable state.  The extra energy is released as an extraordinarily high energy photon called a “gamma ray”.

General formula for isolated Gamma Decay:  $^x_yA^{\ast}\:\longrightarrow\:^x_yA\:+\:^0_0\gamma$

 

Positron Emission:  Radioactive decay that occurs as a result of a proton in the nucleus being converted into a neutron.  The particle released is effectively a high energy positively charged electron called a “positron.”

General formula for Positron Emission:  $^x_yA\:\longrightarrow\:^x_{y-1}B\:+\:^0_1e$

 

Electron Capture:  The nuclear reaction that occurs as a result of an electron from the cloud surrounding the nucleus falling into or “being captured” by the nucleus.  A positively charged proton becomes “neutralized” by the negatively charged electron, effectively converting it into a neutron.

General formula for Electron Capture:  $_y^xA+^{\:\:\:0}_{-1}e\:\left(orbital\:electron\right)\longrightarrow^{\:\:\:\:x}_{y-1}B$

 

 

Particles Found in Nuclear Reactions

Particle	Symbol		Particle	Symbol
Neutron	$^1_0n$		Alpha particle	$^4_2\alpha\:\:\:\:or\:\:\:\:^4_2He$
Proton	$^1_1p\:\:\:or\:\:\:^1_1H$		Beta Particle	$^{\:\:0}_{-1}\beta\:\:\:\:or\:\:\:\:^{\:\:0}_{-1}e$
Electron	$^{\:\:0}_{-1}e$		Positron	$^0_1e$

 

 

 

Nuclear transmutations:  Forced nuclear reactions achieved by bombarding (striking) a nucleus with a neutron or another nucleus.  These reactions are also sometimes referred to as “bombardment reactions.”

 

Condensed Notation for Bombardment Reactons

As a nuclear reaction equation, the above would be expressed as follows:

$^{14}_{\:7}N+^4_2He\longrightarrow^{17}_{\:8}O+^1_1H$

 

Equations for Rate of Nuclear Decay

$Rate=kN$
Where “k” is the rate constant (also called the nuclear decay constant) and N is the number of radioactive nuclei

The SI unit for rate is the Becquerel, which means 1 nuclear disintegration per second.  Another common unit is the “curie” or Ci.  1 Ci = 3.7 x 10¹⁰ Bq

 

The formula above can be integrated in the same way as the first order rate law to give the following equation:

$\ln\frac{N_t}{N_0}=-kt$     which can also be written     $\ln N_t=-kt+\ln N_0$
Where “N_t” is the amount of radioactive material after time “t”, "N₀" is the original amount of radioactive material, "k" is the nuclear decay constant, and "t" is the amount of time that the substance have decayed.

 

 

The decay constant can be determined by the half-life of the radioactive substance using the following equation:

$k=\frac{\ln2}{t_{1/2}}$

Where “t_1/2” is the half-life and "k” is the nuclear decay constant.

Note:  “t_1/2” does NOT mean that you multiply t by 1/2.

 

 

Mass-Energy Conversion

When nuclear reactions occur, a small amount of mass is annihilated and converted into energy.  Albert Einstein discovered that the relationship between the mass annihilated and the energy produced is as follows:

$E=\Delta mc^2$
Where “E” is the energy released, “m” is the mass destroyed or “mass defect”, and c is the speed of light.