5.4 Half-Life of a Radioisotope - PowerPoint Presentation

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5.4 Half-Life of a Radioisotope

The age of the Dead Sea Scrolls was determined using carbon-14.

Learning Goal Given the half-life of a radioisotope, calculate the amount of radioisotope remaining after one or more half-lives.

Half-Life

The

half-life of a radioisotope is the time for the radiation level to decrease (decay) to one-half of the original value.

Decay Curves

The

decay curve for I-131 shows that one-half the sample decays every8 days.

Core Chemistry Skill

Using

Half-Lives

The decay curve

for iodine-131

shows that one-half of the

radioactive sample decays and one-half remains radioactive after each half-life of 8 days.

Half-Lives of Some Radioisotopes

Guide to Using Half-Lives

Half-Life Calculations

The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after 152.4 years?

STEP 1 State the given and needed quantities. ANALYZE Given NeedTHE PROBLEM 36 mg 152.4 yrs milligrams Sr-90 Sr-90 half-life = 38.1 yrs

Half-Life Calculations

The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after 152.4 years?

STEP 2 Write a plan to calculate unknown quantity. years number of half-lives mg Sr-90 mg Sr-90 remaining

Half-life

Number of

half-lives

Half-Life Calculations

The radioisotope strontium-90 has a half-life of 38.1 years. If

a sample contains 36 mg of Sr-90, how many milligrams will remain after 152.4 years?STEP 3 Write the half-life equality and conversion factors.

The radioisotope strontium-90 has a half-life of 38.1 years. If

a

sample contains 36 mg of Sr-90, how many milligrams will remain after 152.4 years?STEP 4 Set up the problem to calculate the needed quantity. 1 half-life 2 half-lives 3 half-lives 4 half-lives 36 mg  18 mg  9 mg  4.5 mg  2.2 mg Sr-90

Half-Life Calculations

Study Check

Carbon-14 was used to determine the age of the Dead Sea Scrolls.

If the Dead Sea Scrolls were determined to be2000 years old and the half-life of carbon-14 is 5730 years, what fractionof this half-life has passed?

Solution

Carbon-14 was used to determine the age of the Dead Sea Scrolls. If the Dead Sea Scrolls were determined to

be2000 years old and the half-life of carbon-14 is 5730 years, what fraction of this half-life has passed?STEP 1 State the given and needed quantities. ANALYZE

Given

Need

THE PROBLEM

2000

yrs

old

fraction of C-14 half-life = 5730 yrs half-life passed

Solution

Carbon-14 was used to determine the age of the Dead Sea Scrolls. If the Dead Sea Scrolls were determined to

be2000 years old and the half-life of carbon-14 is 5730 years, what fraction of this half-life has passed?STEP 2 Write a plan to calculate unknown quantity. years fraction of half-lifeSTEP 3 Write the half-life equality and conversion factors.

Half-life

Solution

Carbon-14 was used to determine the age of the Dead Sea Scrolls. If the Dead Sea Scrolls were determined to

be2000 years old and the half-life of carbon-14 is 5730 years, what fraction of this half-life has passed?STEP 4 Set up the problem to calculate the needed quantity.

Study Check

The half-life of I-123 is 13 h.

How much of a 64-mg sample of I-123 is left after 26 hours?A. 32 mgB. 16 mgC. 8 mg

Solution

The half-life of I-123 is 13 h.

How much of a 64-mg sample of I-123 is left after 26 hours?STEP 1 State the given and needed quantities. STEP 2 Write a plan to calculate unknown quantity. hours number of half-lives

mg

of I-123

mg

of I-123 remaining

ANALYZE Given NeedTHE PROBLEM 26 h 64 mg I-123 mg of I-123 I-123

half-life = 13

hours remaining

Half-life

Number

of

half-lives

The half-life of I-123 is 13 h. How much of a 64-mg sample of

I-123 is left after 26 hours?

STEP 3 Write the half-life equality and conversion factors. STEP 4 Set up the problem to calculate the needed quantity. 1 half-life 2 half-lives

64 mg

 32 mg  16 mg I-123 Answer is B.

Solution