Edexcel IGCSE Physics: Double Science 复习笔记:7.2.2 Half-Life

Edexcel IGCSE Physics: Double Science 复习笔记:7.2.2 Half-Life

Half-Life

 

  • It is impossible to know when a particular unstable nucleus will decay
  • But the rate at which the activity of a sample decreases can be known
    • This is known as the half-life

     

  • Half-life is defined as:

 

The time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half

 

  • In other words, the time it takes for the activity of a sample to fall to half its original level
  • Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length

 

 

Using Half-life

  • Scientists can measure the half-lives of different isotopes accurately:
  • Uranium-235 has a half-life of 704 million years
    • This means it would take 704 million years for the activity of a uranium-235 sample to decrease to half its original amount

     

  • Carbon-14 has a half-life of 5700 years
    • So after 5700 years, there would be 50% of the original amount of carbon-14 remaining
    • After two half-lives, or 11 400 years, there would be just 25% of the carbon-14 remaining

     

  • With each half-life, the amount remaining decreases by half

 

 

Half-Life Graph, downloadable AS & A Level Physics revision notes

 

The diagram shows how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed

 

  • The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life
  • It is the same length of time as it would take to decrease from 50 % activity to 25 % activity
  • The half-life is constant for a particular isotope

 

 

Calculating Half-Life

 

  • To calculate the half-life of a sample, the procedure is:
    • Measure the initial activity, A0, of the sample
    • Determine the half-life of this original activity
    • Measure how the activity changes with time

     

  • The time taken for the activity to decrease to half its original value is the half-life

 

 

Worked Example

The radioisotope technetium is used extensively in medicine. The graph below shows how the activity of a sample varies with time.Worked Example - Half Life Curve, downloadable AS & A Level Physics revision notesDetermine the half-life of this material.

 

Step 1: Draw lines on the graph to determine the time it takes for technetium to drop to half of its original activity

8.2.3-Worked-Example-Half-Life-Curve-Ans-a

 

 

Step 2: Read the half-life from the graph

    • In the diagram above the initial activity, A0, is 8 × 107 Bq
    • The time taken to decrease to 4 × 107 Bq, or ½ A0, is 6 hours
    • The time taken to decrease to 2 × 107 Bq is 6 more hours
    • The time taken to decrease to 1 × 107 Bq is 6 more hours
    • Therefore, the half-life of this isotope is 6 hours

     

 

Worked Example

A particular radioactive sample contains 2 million un-decayed atoms. After a year, there is only 500 000 atoms left un-decayed.What is the half-life of this material?

 

Step 1: Calculate how many times the number of un-decayed atoms has halved

    • There were 2 000 000 atoms to start with
    • 1 000 000 atoms would remain after 1 half-life
    • 500 000 atoms would remain after 2 half-lives
    • Therefore, the sample has undergone 2 half-lives

     

 

Step 2: Divide the time period by the number of half-lives

    • The time period is a year
    • The number of half-lives is 2
    • 1 year divided by 2 is half a year or 6 months
    • Therefore, the half-life is 6 months

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