Section 2: Radioactive Decay

Unstable nuclei can break apart spontaneously, changing the identity of atoms.

KWhat I Know

WWhat I Want to Find Out

LWhat I Learned

• 12(B) Describe radioactive decay process in terms of balanced nuclear equations.

• 2(H) Organize, analyze, evaluate, make inferences, and predict trends from data.

• 2(I) Communicate valid conclusions supported by the data through methods such as lab reports, labeled drawings, graphs, journals, summaries, oral reports, and technology–based reports.

• 12(A) Describe the characteristics of alpha, beta, and gamma radiation.

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Essential Questions

• Why are certain nuclei radioactive?• How are nuclear equations balanced?• How can you use radioactive decay rates to analyze samples of radioisotopes?

Radioactive DecayCopyright © McGraw-Hill Education

Review•radioactivity

New• transmutation• nucleon• strong nuclear force• band of stability• positron emission• positron• electron capture• radioactive decay series• half-life• radiochemical dating

Radioactive DecayCopyright © McGraw-Hill Education

Vocabulary

Nuclear Stability• Except for gamma radiation, radioactive decay involves

transmutation, or the conversion of an element into another element.

• Protons and neutrons are referred to as nucleons.

• All nucleons remain in the dense nucleus because of the strong nuclear force.

• The strong nuclear force acts on subatomic particles that are extremely close together and overcomes the electrostatic repulsion among protons.

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Nuclear Stability• As atomic number increases, more and more neutrons are needed to

produce a strong nuclear force that is sufficient to balance the electrostatic repulsion between protons.

• Neutron to proton ratio increases gradually to about 1.5:1.

Radioactive DecayCopyright © McGraw-Hill Education

Nuclear Stability• The area on the graph within

which all stable nuclei are found is known as the band of stability.

• All radioactive nuclei are found outside the band.

• The band ends at Pb-208; all elements with atomic numbers greater than 82 are radioactive.

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Types of Radioactive Decay

Atoms can undergo different types of decay—beta decay, alpha decay, positron emission, or electron captures—to gain stability.

• In beta decay, radioisotopes above the band of stability have too many neutrons to be stable.

• Beta decay decreases the number of neutrons in the nucleus by converting one to a proton and emitting a beta particle.

Radioactive DecayCopyright © McGraw-Hill Education

Types of Radioactive Decay• In alpha decay, nuclei with more

than 82 protons are radioactive and decay spontaneously.

• Both neutrons and protons must be reduced.

• Emitting alpha particles reduces both neutrons and protons.

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Types of Radioactive Decay

Nuclei with low neutron to proton ratios have two common decay processes.

• A positron is a particle with the same mass as an electron but opposite charge.

• Positron emission is a radioactive decay process that involves the emission of a positron from the nucleus.

• During positron emission, a proton in the nucleus is converted to a neutron and a positron, and the positron is then emitted.

• Electron capture occurs when the nucleus of an atom draws in a surrounding electron and combines with a proton to form a neutron.

Radioactive DecayCopyright © McGraw-Hill Education

Types of Radioactive Decay

Radioactive DecayCopyright © McGraw-Hill Education

Types of Radioactive Decay

Interactive Table

FPO

Add link to Interactive Table from page 868 here.

Radioactive DecayCopyright © McGraw-Hill Education

Writing and Balancing Nuclear Equations

Nuclear reactions are expressed by balanced nuclear equations.

• In balanced nuclear equations, mass numbers and charges are conserved.

Ex. A plutonium-238 atom undergoes alpha decay, write a balanced equation for this decay.

Radioactive DecayCopyright © McGraw-Hill Education

Radioactive DecayCopyright © McGraw-Hill Education

BALANCING A NUCLEAR EQUATION

EVALUATE THE ANSWERThe correct formula for an alpha particle is used. The sums of the superscripts andsubscripts on each side of the equation are equal. Therefore, the charge and themass number are conserved. The nuclear equation is balanced.

Use with Example Problem 1.

Problem NASA uses the alpha decay of plutonium-238 () as a heat source on spacecraft. Write a balanced equation for this decay.ResponseANALYZE THE PROBLEMYou are given that a plutonium atom undergoes alpha decay and forms an unknown product. Plutonium-238 is the initial reactant, while the alpha particle is one of the products of the reaction.

KNOWN

reactant: plutonium-238 ()

decay type: alpha particle emission ()

SOLVE FOR THE UNKNOWN• Apply the conservation of mass number.

238 = A + 4 • Solve for A.

A = 238 - 4 = 234Thus, the mass number of X is 234.• Write the balanced nuclear equation.The periodic table identifies the element as uranium (U). → +

UNKNOWN

mass number of the product A = ?

atomic number of the product Z = ?reaction product X = ?

Radioactive Series

A series of nuclear reactions that begins with an unstable nucleus and results in the formation of a stable nucleus is called a radioactive decay series.

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Radioactive Decay Rates

A half-life is the time required for one-half of a radioisotope to decay into its products.

• Radioactive decay rates are measured in half-lives.

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N is the remaining amount.

N0 is the initial amount.

n is the number of half-lives that have passed.

t is the elapsed time and T is the duration of the half-life.

Radioactive Decay Rates

Radioactive DecayCopyright © McGraw-Hill Education

Radioactive Decay Rates

The process of determining the age of an object by measuring the amount of certain isotopes is called radiochemical dating.

• Carbon-dating is used to measure the age of artifacts that were once part of a living organism.

Radioactive DecayCopyright © McGraw-Hill Education

Radioactive DecayCopyright © McGraw-Hill Education

CALCULATING THE AMOUNT OF REMAINING ISOTOPE

Use with Example Problem 2.

Problem Krypton-85 is used in indicator lights of appliances. The half-life of krypton-85 is 11 y. How much of a 2.000-mg sample remains after 33 y?

ResponseANALYZE THE PROBLEMYou are given a known mass of a radioisotope with a known half-life. You must first determine the number of half-lives that passed during the 33-year period. Then, usethe exponential decay equation to calculate the amount of the sample remaining.

KNOWN

Initial amount = 2.000 mg

Elapsed time (t) = 33 y Half-life (T ) = 11 y

UNKNOWN

Amount remaining = ? mg

Radioactive DecayCopyright © McGraw-Hill Education

CALCULATING THE AMOUNT OF REMAINING ISOTOPE

EVALUATE THE ANSWER

Three half-lives are equivalent to , or . The answer (0.25 mg) is equal to of the initial amount. The answer has two significant figures because the number of years has two significant figures. n does not affect the number of significant figures.

SOLVE FOR THE UNKNOWN

• Determine the number of half-lives passed during the 33 y.

Number of half-lives (n) =

• Substitute t = 33 y and T = 11 y.

• Write the exponential decay equation.

Amount remaining = (initial amount)()n

• Substitute initial amount = 2.000 mg and n = 3.

Amount remaining = (2.000 mg)()3.0

Amount remaining = (2.000 mg)() = 0.2500 mg

Radioactive DecayCopyright © McGraw-Hill Education

Review

Essential Questions

• Why are certain nuclei radioactive?• How are nuclear equations balanced?• How can you use radioactive decay rates to analyze samples of radioisotopes?

Vocabulary• transmutation• nucleon• strong nuclear

force• band of stability

• positron emission

• positron• electron capture• radioactive

decay series

• half-life• radiochemical

dating