Nuclear Decay and Half-Life

What is Nuclear Radiation? Marie Curie and her Husband are credited with explaining the nature of radioactive material. Curie won a Nobel Prize in physics for her discovery of Radium. For her efforts she died from exposure to the very subject she devoted her life. Radiation is the emission of high energy particles from the nucleus of the atom.

Alpha Particles Alpha particles are essentially Helium Nuclei emitted from the nucleus of larger, unstable atoms. We can represent alpha particles in nuclear equations as Alpha particles have the lowest penetration power of any other radioactive material. They have the highest ionization potential, however. This means they can create/break bonds in molecules rather easily. Your skin, clothes, or even air in some cases, can protect you from alpha particle emission.

Beta Particles Beta particles are electrons emitted from the NUCLEUS of the atom. They differ from the traditional electrons that are found in the electron cloud of the atom. These are formed when neutrons decay into protons and electrons. The protons remain in the nucleus while the electrons are expelled as Beta particles. Beta particles have higher penetrative power than alpha particles but lower ionization energy. Wood or cement walls are necessary to protect yourself from Beta particles.

Gamma Rays Gamma rays have no mass. They are forms of high energy electromagnetic radiation expelled from the nucleus of an atom. They also have no charge. Gamma rays can be understood to be simply waves or particles known as photons. Gamma rays are the most penetrative, but have no oxidation potential. I.E. they can only be blocked by extremely thick lead shielding but they cannot cause changes to bonds between atoms.

Transmutation Transmutation comes from an old word Alchemists would use to describe the process of changing one material into another; often lead to gold. In Chemistry this can really happen with Radioactive materials. As materials are bombarded with radiation or as they emit radiation, they become entirely different atoms. For example, if Uranium 238 were to emit an alpha particle, it would become Thorium-234

Half-Life Half life is the amount of time for half of a radioactive substance to decay. For example, Carbon-14 has a half life of 5735 years. if I had a 100g sample of Carbon-14 today, and came back in 5735 years, I would have 50g of Carbon-14 left and 50g of some new atom. (An isotope of Nitrogen.) How much carbon and nitrogen isotope would I have left if I came back in another 5735 years?

Parent/Daughter Atoms We can refer to the still radioactive samples as the “parent” atoms. The atoms left behind after decay can be called daughter atoms. In the previous example, the Carbon-14 was the parent atom and the Nitrogen isotope was the daughter.

Simplified Half-Life Formula 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑝𝑎𝑟𝑒𝑛𝑡 𝑎𝑡𝑜𝑚𝑠 𝑙𝑒𝑓𝑡= 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑝𝑎𝑟𝑒𝑛𝑡 𝑎𝑡𝑜𝑚 2 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑎𝑙𝑓−𝑙𝑖𝑣𝑒𝑠 So, let’s give all of these quantities their own variable. Mass of parent atoms left = m Original mass of radioactive isotope = o Number of half lives = n Our equation becomes 𝑚= 𝑜 2 𝑛

Sample An unknown isotope has a half life of 30 minutes. If I start with 50g, how much will I have left in 2 hours? First: Figure out our value for n in the equation. How many half lives will elapse in the given amount of time? In this problem a half-life is 30 minutes and we are given 2 hours of total time. How many half lives are there in 2 hours? 2 hours is 120 minutes, 120 divided by 30 is 4. So our value for n is 4. We already know the value for o, it’s 50g. We are looking for m. Put the numbers into the equation to figure it out. 𝑚= 50 4 2 = 50 16 =3.125𝑔

Sample 2 Uranium-239 has a half life of 4 billion years. One of the oldest planets in the universe is 16 billion years old. If this planet originally contained 4,000,000 tons of Uranium, how much is left? First find out how many half lives have occurred. N= 16billion/4billion = 4 Our original amount is 4,000,000 tons. This is our o Plug everything into the equation 𝑚= 4,000,000 4 2 = 250,000 tons

NOTE If a problem asks you, “What fraction is left,” you can use the same formula. Instead of inputting a value for o, use the number one. Whatever your n^2 becomes, will give you your fraction. (Lets look at problem 1 on your assignment.)