Mr. Braswell's Chemistry Help

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                                          NUCLEAR CHEMISTRY


Radioactivity is the result of a natural change of an isotope.

1.  (Note: in nuclear chemistry, element symbols are traditionally preceded by their atomic weight (upper left) and atomic number (lower left). see table O.

reference tables

2.  Beta Radiation is the transmutation of a neutron into a proton and a electron (followed by the emission of the electron from the atom's nucleus: particle-beta ).

When an atom emits a β particle, the atom's mass will not change (since there is no change in the total number of nuclear particles), however the atomic number will increase by one (because the neutron transmutated into an additional proton).

An example of this is the decay of the isotope of carbon named carbon-14 into the element nitrogen:

arrow 0

3.  Gamma Radiation (γ) involves the emission of electromagnetic energy (similar to light energy) from an atom's nucleus.

No particles are emitted during gamma radiation, and thus gamma radiation does not itself cause the transmutation of atoms, however γ radiation is often emitted during, and simultaneous to, α or β radioactive decay. X-rays, emitted during the beta decay of cobalt-60, are a common example of gamma radiation.

Various types of radiation maybe be found on table N of your reference tables.

reference tables

Animation of Fissioning of 235U

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                                                  Radioactive Decay

There are three types of natural radioactive decay. They are alpha emisson, beta emission, and gamma emission.

    alpha emisson

1.  Alpha emission results in releasing an alpha particle.

2.  An alpha particle has two protons and two neutrons, so it has a positive charge.

(Since it has two protons it is a helium nucleus.)

3.  It is written in equations like this:

alpha particle

 beta emission

1.  Beta emission is when a high speed electron (negative charge) leaves the nucleus.

2.  Beta emission occurs in elements with more neutons than protons, so a neutron splits into a proton and an electron.

3.  The proton stays in the nucleus and the electron is emitted.

4.  Negative electrons are represented as follows:


 gamma emission

1.  Gamma Emission is when an excited nucleus gives off a ray in the gamma part of the spectrum.

2.  A gamma ray has no mass and no charge.

3.  This often occurs in radioactive elements because the other types of emission can result in an excited nucleus.

4.  Gamma rays are represented with the following symbol.

gamma ray symbol 

Positron emission

The two types of artificial radiation are positron emission and electron capture.

1.  Positron emission involves a particle that has the same mass as an electron but a positive charge.

2.  The particle is released from the nucleus.


 electron capture

1.  Electron capture is when an unstable nucleus grabs an electron from its inner shell to help stabilize the nucleus.

2.  The electrons combine with a proton to form a neutron which stays in the nucleus.

Electron Capture

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                               Nuclear Equations

Nuclear notations are used to represent the decay of one element into another. The generic formula for a radioactive element is as follows:

Generic Equation

Some examples of nuclear decay equations are:

 example one


example two  

Nuclear Bombardment Reactions

Bombardment reactions involve the nucleus of the atom being bombarded (hence the name) with particles from the nucleus or an entire nucleus.

Examples of the particles are neutrons and alpha particles.

These reactions usually give off a different particle than the one that they were bombarded with.

Here is an example equation for a bombardment reaction.

bombardment example

Particle accelerators are where most of the bombarding takes place. The accelerators move the particles toward each other at great

Go to Balancing Nuclear Equations

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Radioactive decay proceeds according to a principal called the half-life.

The half-life (T½) is the amount of time necessary for one-half of the radioactive material to decay.

For example, the radioactive element bismuth (210-Bi) can undergo alpha decay to form the element thallium (206-Tl) with a reaction half-life equal to five days.

If we begin an experiment starting with 100 g of bismuth in a sealed lead container, after five days we will have 50 g of bismuth and 50 g of thallium in the jar.

After another five days (ten from the starting point), one-half of the remaining bismuth will decay and we will be left with 25 g of bismuth and 75 g of thallium in the jar.

As illustrated, the reaction proceeds in halfs, with half of whatever is left of the radioactive element decaying every half-life period.

decay-graph - Radioactive Decay of Bismuth-210 (T½ = 5 days)

Radioactive Decay of Bismuth-210 (T½ = 5 days)

Half life formulas are found on table T of your reference tables.

The formula to calculate the fraction remaining is in table T

fraction remaining = (1/2)t/T

t = total time elapsed

T = half-life

number of half-life periods = t/T

For example, Bi-210 can undergo a decay to Tl-206 with a T½ of five days.

Bi-215, by comparison, undergoes b decay to Po-215 with a T½ of 7.6 minutes, and Bi-208 undergoes yet another mode of radioactive decay (called electron capture) with a T½ of 368,000 years!

  The formula to calculate the mass of the sample remaining is in table T

mass of sample remaining = (1/2)t/T (mass of original sample)

Example 1

Consider a 100g sample of C-14. (C-14 decays into N-14)


After 0 half-life or 0 years there will be 100 g of C-14 and 0 g of N-14 (the decay product) fraction of C-14 remaining = (1/2)0/5730 (100g) = (1/2)0 (100g) = 100g


After 1 half-life or 5730 years there will be 50 g of C-14 and 50 g of N-14

fraction of C-14 remaining = (1/2)5730/5730 (100g) = (1/2)1 (100g) = 50g


After 2 half-life or 2(5730 years) there will be 25 g of C-14 and 75 g of N-14

fraction of C-14 remaining = (1/2)11460/5730 (100g) = (1/2)2 (100g) = 25g


After 3 half-life or 3(5730 years) there will be 12.5 g of C-14 and 87.5 g of N-14

fraction of C-14 remaining = (1/2) 17190/5730 (100g) = (1/2)3 (100g) = 12.5g


Example 2

What will remain of a 50 g sample of phosphorus-32 after 1716 hours?


Mass of original sample = 50 g

T = 14.3 d

t = 1716 hours or 71.5 d


fraction remaining = (1/2)t/T = (.5)71.5 d/14.3 d = (.5)5 =  0.03125

mass of P-32 remaining =  (1/2)t/T (mass of original sample) = (0.03125) (50g) = 1.56 g

Go to half-life problems



No one can say for sure when a particular nucleus will decay but one can predict how many in a given sample will decay over time.

Radioactive elements have a half-life.

The half life of any given element is the time that is required for one half of the sample to decay.

So if you have 10 grams of a radioactive element, after one half-life there will be 5 grams of the radioactive element left.

After another half-life, there will be 2.5 g of the original element left, after another half-life, 1.25 g will be left.

The equation for half-life calculations is as follows:

Half life equation

  • AE is the amount of substance left
  • A0 is the original amount of substance
  • t is the elasped time
  • t1/2 is the half-life of the substance

Other variations on the half-life equation are as follows:

time equation

half life equation

An example problem is if you originally had 157 grams of carbon-14 and the half-life of carbon-14 is 5730 years, how much would there be after 2000 years?

example one

There would be 123 grams left.


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                                                Nuclear Reactions

 Animation of a chain reaction fissioning many 235U atoms

While many elements undergo radioactive decay naturally, nuclear reactions can also be stimulated artificially.

Although these reactions also occur naturally, we are most familiar with them as stimulated reactions.

There are two such types of nuclear reactions:

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                                Nuclear fission

Nuclear fission: reactions in which an atom's nucleus splits into smaller parts, releasing a large amount of energy in the process.

Most commonly this is done by "firing" a neutron at the nucleus of an atom.

The energy of the neutron "bullet" causes the target element to split into two (or more) elements that are lighter than the parent atom.

fission reaction - The Fission Reaction of Uranium-235

The Fission Reaction of Uranium-235

The Fission of U-235
Concept simulation - Illustrates a nuclear fission reaction.

During the fission of U-235, three neutrons are released in addition to the two daughter atoms.

If these released neutrons collide with nearby U-235 nuclei, they can stimulate the fission of these atoms and start a self-sustaining nuclear chain reaction.

This chain reaction is the basis of nuclear power.

As uranium atoms continue to split, a significant amount of energy is released from the reaction.

The heat released during this reaction is harvested and used to generate electrical energy.

Two Types of Nuclear Chain Reactions
Concept simulation - Reenacts controlled and uncontrolled nuclear chain reactions.

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                                  Nuclear fusion

Nuclear fusion: reactions in which two or more elements "fuse" together to form one larger element, releasing energy in the process.

A good example is the fusion of two "heavy" isotopes of hydrogen (deuterium: H-2 and tritium: H-3) into the element helium.

fusion reaction - Nuclear Fusion of Two Hydrogen Isotopes

Nuclear Fusion of Two Hydrogen Isotopes

Nuclear Fusion 
Concept simulation - Reenacts the fusion of deuterium and tritium inside of a tokamak reactor.
Fusion reactions release tremendous amounts of energy and are commonly referred to as thermonuclear reactions. 
Although many people think of the sun as a large fireball, the sun (and all stars) are actually enormous fusion reactors. 
Stars are primarily gigantic balls of hydrogen gas under tremendous pressure due to gravitational forces
Hydrogen molecules are fused into helium and heavier elements inside of stars, releasing energy that we receive as light and heat.  

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                                                  DECAY SERIES

In nuclear science, the decay chain refers to the radioactive decay of different discrete radioactive decay products as a chained series of transformations.

Most radioactive elements do not decay directly to a stable state, but rather undergo a series of decays until eventually a stable isotope is reached.

Decay stages are referred to by their relationship to previous or subsequent stages.

A parent isotope is one that undergoes decay to form a daughter isotope. The daughter isotope may be stable or it may decay to form a daughter isotope of its own.

The daughter of a daughter isotope is sometimes called a granddaughter isotope.

Nuclear decay may be found on table N of your reference tables.

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                        Balancing Nuclear Equations

reference tables



1. Complete the following nuclear equations:

 (a) ? + 10n ---> 249Bk + 0-1e

 (b) 20Ne + ? ---> 24Mg + g

2. Identify the daughter nucleus in each of the following decays and write the balanced nuclear equation: Where a = alpha decay and b = beta decay.

b decay of tritium

b decay of krypton-87

a decay of protactinium-225



3. Identify the daughter nucleus in each of the following decays and write the balanced nuclear equation:

 b decay of actinium-228

a decay of radon-212

a decay of francium-221

4. Write the balanced nuclear equation for the following radioactive decays:

(a) b decay of nickel-63

(b) a decay of gold-185

5. Write the balanced nuclear equation for the following radioactive decays:

(a) b decay of uranium-233

(b) a decay of polonium-212.

6. Determine the particle emitted and write the balanced nuclear equation for the following nuclear transitions:

(a) sodium-24 to magnesium-24

(b) 128Sn to 128Sb

(c) 228Th to 224Ra.

7. Determine the particle emitted and write the balanced nuclear equation for the following nuclear transitions:

(a) carbon-14 to nitrogen-14; (b) uranium-229 to thorium-225.

8. Write balanced nuclear equations for the reactions described below.

a. Lead-210 decays by beta emission.




b. An Iron-54 is bombarded with an alpha particle to give two protons and another nucleus.

c. Ar-40 is bombarded with another nucleus to produce K-43 and a proton.

d. Some nucleus undergoes alpha decay producing Pa-233

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                                            HALF-LIFE PRACTICE PROBLEMS


1 If 1/8 of an original sample of krypton-74 remains unchanged after 34.5 minutes, what is the half-life of krypton-74?  (1) 11.5 min   (2) 23.0 min   (3) 34.5 min   (4) 46.0 min

2 The fossilized remains of a plant were found at a construction site. The fossilized remains contain 1/16 the amount of carbon-14 that is present in a living plant. Determine the approximate age of these fossilized remains.


3  What is the half-life of sodium-25 if 1.00 gram of a 16.00-gram sample of sodium-25 remains unchanged after 237 seconds?    (1) 47.4 s (2) 59.3 s (3) 79.0 s (4) 118 s

Base your answers to questions 4 and 5 on the information below.

Some radioisotopes used as tracers make it possible for doctors to see the images of internal body parts and observe their functions. The table below lists information about three radioisotopes and the body part each radioisotope is used to study.

4  Write the equation  for the nuclear decay of the radioisotope used to study red blood cells. Include both the atomic number and the mass number for each missing particle.


5  It could take up to 60. hours for a radioisotope to be delivered to the hospital from the laboratory where it is produced. What fraction of an original sample of 24Na remains unchanged after 60. hours?

6 Bromine -82 has a half-life of 36 hours. A sample containing Br-82 was found to have an activity of 1.2 x 105 disintegrations/min.  How many grams of Br-82 were present in the sample? Assume that there were no other radioactive nuclides in the sample.

4. Lead-210 has a half-life of 20.4 years. A counter registers 1.3 x 104 disintegrations in 5 minutes. How many grams of Pb-210 are there?

5. Smoke detectors contain small amounts of americium-241. Am-241 decays by emitting alpha particles and has a decay constant of 1.51 x10-3 yr-1. If a smoke detector gives off to disintegrations per second, how many grams of Am-241 are present in the detector?

6. Krypton-87 has a rate constant of 1.5 x 10-4 sec-1. What is the activity of a 2.0 mg sample? How long would it take for half of this much Krypton-87 in to decay?

7. A sample of a beam from the tomb of an ancient Egyptian pharaoh was analyzed in 2000 and gave 6.0 counts per minute (cpm) in a scintillation counter (a device that can register nuclear emissions.) A sample of freshly cut wood containing the same amount of carbon gave 15.3 cpm. Assuming that Carbon-14 is the decaying nucleus in this case, and that C-14 has a half life of 5730 years, in what year, approximately, did the king die?

8. An oil painting attributed to Rembrandt (1606-1669) is checked by 14C dating. The 14C content (t1/2 14C = 5730 yr.) of the canvas is 0.975 times that of a living plant. Could the painting have been painted by Rembrandt?

 9. Binding energy is given in units of kJ per mole of nuclei. The masses of the following particles may be useful in calculating the binding energies of the following.


1.00866 amu


1.00728 amu


11.00931 amu


6.01512 amu


55.9349 amu


133.9051 amu

 What is the binding energy of Boron-11

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