introduction: the nucleus of some atoms are unstable and this causes them to undergo radioactive decay. this…

introduction: the nucleus of some atoms are unstable and this causes them to undergo radioactive decay. this process always happens at a specific rate for each unstable isotope, and exactly half of the atoms in a sample will decay in that amount of time. the term half - life is what we call the time it takes for exactly half of a radioisotope to decay into another isotope that may or may not be stable as well. this process creates a similar shaped curve for all radioactive decay and there is a mathematical formula that can be used to calculate the amount of the unstable isotope remaining at any time which also gives the shape of the curve as well. the three main types of radioactive decay are alpha (α), beta (β), and gamma (γ). an alpha particle is a helium nucleus composed of two protons and two neutrons (₂⁴he). a beta particle is an electron being emitted from the nucleus after a neutron converts into a proton which releases the electron(₋₁⁰e). gamma radiation has no mass and no charge and is a release of pure energy (γ). because alpha is the largest, it has the least amount of penetrating power, making it the least dangerous. a piece of paper or your skin can stop an alpha particle. beta is much smaller, so it has more penetrating power, but can be stopped by a thin sheet of metal foil. gamma is pure energy so it can penetrate and cause a lot of damage. it takes several inches of lead or several feet of concrete to mostly stop gamma radiation. there are two nuclear processes that release very large quantities of energy. fission is when a large atom is split into smaller atoms, and fusion is when smaller atoms combine into a larger atom. no matter the type of nuclear process or decay, the mass numbers and atomic numbers must be balanced in a nuclear equation. the energy that is released during a nuclear process is the result of the actual masses of the reactants and products not being equal to each other. the mass that is missing from the beginning to the end is called the mass defect, and it is the number that goes into einsteins infamous e = mc² equation. the mass must be measured in kg, the speed of light is a constant 3.00×10⁸ m/s, and the energy output is in joules. even a tiny amount of missing mass will be turned into a very large amount of energy. purpose: the purpose of this lab activity is to show how half - lives work, what the graph of exponential decay looks like, and how to use the mathematical formula that describes both to predict and/or verify data from the lab. pre - lab: 1. (3) fill in the table with the basic information on the three basic types of nuclear radiation\n| radiation | symbol | equation | relative size (s, m, l) | relative strength (h, m, l) | can be stopped by (object) |\n|--|--|--|--|--|--|\n| alpha | α | | | | |\n| beta | β | | | | |\n| gamma | γ | | | | |\n2. (8) in the space to the right, write the nuclear equation for each of the following: a. (1) the alpha decay of iodine - 128 b. (1) the beta decay of germanium - 75 c. (1) the alpha and gamma decay of uranium - 238 d. (1) the beta and gamma decay of francium - 223

introduction: the nucleus of some atoms are unstable and this causes them to undergo radioactive decay. this process always happens at a specific rate for each unstable isotope, and exactly half of the atoms in a sample will decay in that amount of time. the term half - life is what we call the time it takes for exactly half of a radioisotope to decay into another isotope that may or may not be stable as well. this process creates a similar shaped curve for all radioactive decay and there is a mathematical formula that can be used to calculate the amount of the unstable isotope remaining at any time which also gives the shape of the curve as well. the three main types of radioactive decay are alpha (α), beta (β), and gamma (γ). an alpha particle is a helium nucleus composed of two protons and two neutrons (₂⁴he). a beta particle is an electron being emitted from the nucleus after a neutron converts into a proton which releases the electron(₋₁⁰e). gamma radiation has no mass and no charge and is a release of pure energy (γ). because alpha is the largest, it has the least amount of penetrating power, making it the least dangerous. a piece of paper or your skin can stop an alpha particle. beta is much smaller, so it has more penetrating power, but can be stopped by a thin sheet of metal foil. gamma is pure energy so it can penetrate and cause a lot of damage. it takes several inches of lead or several feet of concrete to mostly stop gamma radiation. there are two nuclear processes that release very large quantities of energy. fission is when a large atom is split into smaller atoms, and fusion is when smaller atoms combine into a larger atom. no matter the type of nuclear process or decay, the mass numbers and atomic numbers must be balanced in a nuclear equation. the energy that is released during a nuclear process is the result of the actual masses of the reactants and products not being equal to each other. the mass that is missing from the beginning to the end is called the mass defect, and it is the number that goes into einsteins infamous e = mc² equation. the mass must be measured in kg, the speed of light is a constant 3.00×10⁸ m/s, and the energy output is in joules. even a tiny amount of missing mass will be turned into a very large amount of energy. purpose: the purpose of this lab activity is to show how half - lives work, what the graph of exponential decay looks like, and how to use the mathematical formula that describes both to predict and/or verify data from the lab. pre - lab: 1. (3) fill in the table with the basic information on the three basic types of nuclear radiation\n| radiation | symbol | equation | relative size (s, m, l) | relative strength (h, m, l) | can be stopped by (object) |\n|--|--|--|--|--|--|\n| alpha | α | | | | |\n| beta | β | | | | |\n| gamma | γ | | | | |\n2. (8) in the space to the right, write the nuclear equation for each of the following: a. (1) the alpha decay of iodine - 128 b. (1) the beta decay of germanium - 75 c. (1) the alpha and gamma decay of uranium - 238 d. (1) the beta and gamma decay of francium - 223

Answer

Explanation:

Step1: Recall alpha - decay concept

In alpha - decay, an alpha particle (${2}^{4}He$) is emitted. The mass number of the parent nucleus decreases by 4 and the atomic number decreases by 2. Iodine - 128 has atomic number 53. After alpha - decay, the new element has atomic number $53 - 2=51$ (antimony, Sb) and mass number $128 - 4 = 124$. The nuclear equation is ${53}^{128}I\rightarrow_{51}^{124}Sb + _{2}^{4}He$.

Step2: Recall beta - decay concept

In beta - decay, a neutron in the nucleus converts into a proton and an electron (beta particle, ${ - 1}^{0}e$) is emitted. The mass number remains the same and the atomic number increases by 1. Germanium - 75 has atomic number 32. After beta - decay, the new element has atomic number $32+1 = 33$ (arsenic, As) and mass number 75. The nuclear equation is ${32}^{75}Ge\rightarrow_{33}^{75}As+_{ - 1}^{0}e$.

Step3: Recall alpha and gamma decay concept

For uranium - 238 (atomic number 92), in alpha - decay, it emits an alpha particle (${2}^{4}He$). The new element has atomic number $92 - 2=90$ (thorium, Th) and mass number $238 - 4=234$. Gamma decay is just the release of energy and does not change the mass number or atomic number of the element. The nuclear equation is ${92}^{238}U\rightarrow_{90}^{234}Th+_{2}^{4}He+\gamma$.

Step4: Recall beta and gamma decay concept

Francium - 223 has atomic number 87. In beta - decay, a neutron converts to a proton and an electron is emitted. The new element has atomic number $87 + 1=88$ (radium, Ra) and mass number 223. Gamma decay releases energy without changing the mass number or atomic number. The nuclear equation is ${87}^{223}Fr\rightarrow{88}^{223}Ra+_{ - 1}^{0}e+\gamma$.

For the table in pre - lab part 1:

Radiation Symbol Equation Relative Size (S, M, L) Relative Strength (H, M, L) Can Be Stopped By (Object)
Alpha $\alpha$ ${Z}^{A}X\rightarrow{Z - 2}^{A - 4}Y+_{2}^{4}He$ L L Paper/skin
Beta $\beta$ ${Z}^{A}X\rightarrow{Z + 1}^{A}Y+_{ - 1}^{0}e$ S M Thin metal foil
Gamma $\gamma$ ${Z}^{A}X\rightarrow{Z}^{A}X+\gamma$ - (no mass) H Several inches of lead/several feet of concrete

Answer:

Radiation Symbol Equation Relative Size (S, M, L) Relative Strength (H, M, L) Can Be Stopped By (Object)
Alpha $\alpha$ ${Z}^{A}X\rightarrow{Z - 2}^{A - 4}Y+_{2}^{4}He$ L L Paper/skin
Beta $\beta$ ${Z}^{A}X\rightarrow{Z + 1}^{A}Y+_{ - 1}^{0}e$ S M Thin metal foil
Gamma $\gamma$ ${Z}^{A}X\rightarrow{Z}^{A}X+\gamma$ - (no mass) H Several inches of lead/several feet of concrete

a. ${53}^{128}I\rightarrow{51}^{124}Sb + {2}^{4}He$ b. ${32}^{75}Ge\rightarrow_{33}^{75}As+{ - 1}^{0}e$ c. ${92}^{238}U\rightarrow_{90}^{234}Th+{2}^{4}He+\gamma$ d. ${87}^{223}Fr\rightarrow_{88}^{223}Ra+_{ - 1}^{0}e+\gamma$