Natural Radioactivity Homework Helper


Most elements have isotopes, but not all isotopes are radioactive. Many isotopes are stable variations in mass, occurring naturally.  Unstable isotopes decay into other isotopes and elements, and emit energy which is picked up as radioactivity.


An element is defined by the number of protons it has in its atomic nucleus.  For example, the element hydrogen has one proton in its nucleus.  It has three different isotopes:  hydrogen-1, with one proton and no neutrons in its nucleus; hydrogen-2 (also called deuterium) with one proton and one neutron in its nucleus, and hydrogen-3 (also called tritium), with one proton and 2 neutrons. The number of neutrons determine the type of isotope it is. Similarly, the element oxygen has three stable isotopes, all with 8 protons in its atomic nucleus.  Oxygen-16 has 8 neutrons, oxygen-17 has 9 neutrons, and oxygen-18 has 10 neutrons.

Figure 1: Isotopes differ in the number of neutrons in the atom

Radioactive Isotopes

An element is radioactive if it is unstable and decays into other elements, emitting subatomic particles and energy.  Radioactive elements that occur in nature take so long to decay that they still exist as elements.  For example, the element uranium is naturally radioactive.  One of its isotopes, Uranium-235, has 92 protons and 143 neutrons in its atomic nucleus.  Another isotope, Uranium-238 has 92 protons and 146 neutrons in its atomic nucleus. Other elements are not radioactive naturally have radioactive isotopes that can be produced artificially.

The Half-Life

For example, it takes 4.5 x 109 years for Uranium-238 to decay, and 7.1 x 108 years for Uranium 235 to decay.  Other radioisotopes have much shorter half-lives.  The radioisotope Cesium-137 has a half-life of 30 years.  Starting with a 10 gram sample today, 5 grams would be left in 30 years, 2.5 grams would be left in 60 years, and 1.25 grams in 90 years.

Figure 2:  Example of the measurement of radioactive decay in the number of half-lives.

Carbon Dating

The element carbon exists in all living things, as well as things that once were living.  One of its isotopes, Carbon-14, naturally radioactive, with a half-life of about 5730 years.  In radiocarbon dating, the ratio of Carbon-14 to the other naturally occurring isotopes of carbon, is measured, so the approximate age of the item can be deduced.  The paper of the Dead Sea Scrolls, wood samples from the tombs of Egyptian kings, and prehistoric skeletal remains also some of the many objects that have been studied to estimate their age.

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Radioactive elements have a half-life. Half-life occurs naturally in some of the radioactive elements while it could be artificially stimulated in some other elements.

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

For example:  If you have 10 grams of a radioactive element to start with….. 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.

Number of

Each and every radioactive element has its own half-life. For instance, 238U has a half-life of 4.5billion years.


A radioactive substance has a half-life of 20 minutes. If we begin with a 500 g sample, how much of the original sample remains after two hours?

Two hours is 120 minutes -> six half-lives. At the end of the stated time period, 7.8 g remains.

500 g -> 250 g -> 125 g -> 62.5 g -> 31.25 g -> 15.625 g -> 7.8125 g

7.8 g remains

Another interesting fact is half-life of 14C is 5730 years and this is very helpful in geological dating of any archaeological material. (CARBON DATING)


The ratio of normal carbon (carbon-12) to carbon-14 in the air and in all living things at any given time is nearly constant. At this moment, your body has a certain percentage of carbon-14 atoms in it, and all living plants and animals have the same percentage.

­As soon as a living organism dies, it stops taking in new carbon. The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample. By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely.

Three types of natural radioactive decay include alpha radiation, beta radiation and gamma radiation.

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