Half-Life and Radioactivity

Radioactivity and Half-Life

• Radioactive decay is when an unstable nucleus breaks apart into smaller pieces
  • This occurs spontaneously, randomly, and naturally
  • The nucleus gives off small particles
    • Alpha particles (helium nuclei)
    • Neutrons
    • Protons (rare)
  • Energy is also generally released
    • Gamma (radiation only, no mass)
    • Beta (electrons from just outside the nucleus)
• Some scientists involved in early research into radioactivity
  • Henri Bacquerel, Ernest Rutherford, Paul Villard, Pierre Curie, Marie Curie
• Half-Life is the amount of time it takes for a material to decay by half
  • EX: If you have 20 grams of a radioactive material and it decays to 10 grams in 4 days, then the half-life is 4 days. In another 4 days, there will be 5 grams left.
  • Half-life is abbreviated as t_½
  • The unit for t½ depends on the material
• The amount of material remaining can be found in two ways
  • Create and use a half-life chart
  • Use the formula (n = number of half-lives)

Positive Uses of Some Radioactive Elements

Isotope	Use
131I	diagnosis and treatment of thyroid disorders
14C / 12C Ratio	dating once-living organisms
236U / 206Pb Ratio	geological dating
60Co	cancer treatment

 

Half-Life Charts

 

Number of Half-Lives	Amount of Substance Remaining
	As a Fraction	As a Percent
0	1/1	100%
1	1/2	50%
2	1/4	25%
3	1/8	12.5%
4	1/16	6.25%
5	1/32	3.125%
6	1/64	1.5625%

   

Other Types of Problems

• You make one column for the number of half-lives
  • Always start at zero.
• Make another column for amount of material
  • This may be any form of “amount”
    • Fraction (start at 1/1)
    • Percent (start at 100%)
    • Mass (start at the total mass)
  • Amounts decrease BY HALF (divide by 2) as the number of half-lives increases
• Make another column for time passing
  • Time can be in any unit
    • Always start at zero.
  • Time increases BY ITSELF
    • Ex: if half-life is 3 days, then the times are 3, 6, 9, 12 …
    • Ex: if half-life is 13 hours, then the times are 13, 26, 39 …

You have 68 grams of a radioactive material. It undergoes 4 half-lives. How much material remains?

Number of Half-Lives	Amount of Substance Remaining
	Fraction	Percent	Mass (g)
0	1/1	100%	68
1	1/2	50%	34
2	1/4	25%	17
3	1/8	12.5%	8.5
4	1/16	6.25%	4.25

 

Determining the Number of Half-Life

• Determining the number of half-lives
  • What you need:
    • The half-life of the material
    • The total amount of time
• Determining the amount of time passed
  • What you need:
    • The half-life of the material
    • The number of half-lives
• Determining the amount of starting material
  • What you need:
    • The number of half-lives
    • The amount of material you currently have
• Determining the half-life of the material
  • What you need:
    • The total amount of time
    • The percentage (or fraction) of material you currently have
• There are other variations. You just need to reason them out.
  • In most cases, a half-life chart will help

A radioactive material has a half-life of 23 days. If you measure it 207 days later, how many half-lives did it undergo?

• You can solve this more than one way:
  • Create a half-life chart
  • Use math
  • total time divided by the half-life
  • half-lives
   

# Half-Lives	Total Time (days)
0	0
1	23
2	46
3	69
4	92
5	115
6	138
7	161
8	184
9	207 (stop here)

   

Determining the Amount of Time Passed

A radioactive material has a half-life of 12.5 days. If it undergoes 6 half-lives, how much time passes?

• You can solve this more than one way:
  • Create a half-life chart
  • Use math
    • half-life x # half-lives
    • 12.5 x 6 = 75 days

 

# Half-Lives	Total Time (days)
0	0
1	12.5
2	25
3	37.5
4	50
5	62.5
6	75

Determining the Amount of Starting Substance

A radioactive material has a half-life of 8 days. If you have 13 grams after 32 days, how much was there in the beginning?

• You can solve this more than one way:
  • Create a half-life chart
    • Work down to find the # of half-lives, then work up to find the amount
  • Use math
    • Find out how many half-lives
    • ³²/₈ = 4 half-lives
      • Use 13 x 2ⁿ = 13 x 2⁴ = 13 X 16 = 208 grams

 

# Half-Lives	Total Time (days)	Amount of Material (grams)
0	↓ 0	208
1	↓ 8	↑ 104
2	↓ 16	↑ 52
3	↓ 24	↑ 26
4	32 →	↑ 13

 

Determining the Half-Life of a Material

You have 12.5% of a radioactive material remaining after 36 hours. What is the half-life of the material?

• You can solve this more than one way:
  • Create a half-life chart
    • Find the number of half-lives
    • Divide total time by number of half-lives
  • Use math
    • 12.5% = → = → 8 = 2ⁿ
    • 8 = 2ⁿ → 8 = 23 therefore, n = 3  
    • = 12 hours

# Half-Lives	% Material	Total Time (hours)
0	↓ 100	0
1	↓ 50	↑ 12
2	↓ 25	↑ 24
3	12.5 →	↑ 36

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