Radioactivity and Half life

1
Radioactivity and Half life
2
HIGHER GRADE CHEMISTRY CALCULATIONS

• Radioactivity and Half-Life

• Half-life is the time taken for half of a
  radioisotope to decay. This value is constant
  for that particular radioisotope.
• Usually questions about radioactivity involve
• Half-life
• The time over which the radioactivity has been
  measured
• The quantity or intensity of the radiation.

Worked example 1. A radioisotope has a half-life
of 4 days. The radioisotope had an initial count
rate of 800 counts per minute. What will be the
count rate after 16 days?
At start count rate 800 counts min-1.
After 4 days 400 counts min-1.
After 8 days 200 counts min-1.
After 12 days 100 counts min-1.
After 16 days 50 counts min-1.
3

• Worked example 2.
• Thallium-208 has a half life of 3.1 minutes and
  decays by beta emission to form a stable isotope.
• What mass of a 2.08 g sample of Tl-208 will
  remain unchanged after
• 9.3 minutes?
• (b) How many atoms will have decayed.
• (c) Identify the stable isotope formed by the
  decay of Tl-208 by beta emission.

(a) At start mass 2.08g
After 3.1 days 1.04g
After 6.2 days 0.52g
After 9.3 days 0.26g
(b) At start no. of atoms 2.08/208 x 6.02 x
1023 6.02 x 1021
After 3.1 days no. of atoms of Tl-208 left
undecayed 3.01 x 1021
After 6.2 days no. of atoms of Tl-208 left
undecayed 1.505 x 1021
After 9.3 days no. of atoms of Tl-208 left
undecayed 0.7525 x 1021
No. of atoms of Tl-208 which have
decayed 6.02 x 1021 -0.7525 x 1021.
5.2675 x 1021

Higher Grade Chemistry
(c) Pb-208 has been formed.
4

• Calculations for you to try.
• Th-234 has a half-life of 24.1 days. What mass
  of a 20.4g sample will remain after 96.4 days?

At start mass 20.4 g
After 24.1 days mass left 10.2 g
After 48.2 days mass left 5.1 g
After 72.3 days mass left 2.55 g
After 96.4 days mass left 1.275 g

• A sample of Pu-242 has a mass of 1.21 g.
• (a) How many atoms of Pu-242 are there in
  the sample?
• (b) How many atoms of Pu-242 will remain
  after 3 half lives.
• (c) Use the half life in the data book
  for Pu-242 to calculate the time it would take to
  reduce the number of Pu-242 atoms in the sample
  to 1/8 of its original value.

(a) No of atoms 1.21/242 x 6.02 x 1023.
3.01 x 1021

• 1/8 of original value means that 3 half lives
  have passed.
• 3 x 3.79 x 105 years 1.137 x 106 years

Higher Grade Chemistry
5

• Calculations for you to try.
• The count rate due to carbon-14 in ancient wooden
  timber was found to be
• 100 counts per minute. A sample of
  modern wood had a count rate of 1600 counts per
  minute. Given that carbon-14 has a half life of
  5570 years, calculate the age of the ancient
  timber.

At start count rate 1600 counts min-1.
After 1 half-life 800 counts min-1.
After 2 half-life 400 counts min-1.
After 3 half-life 200 counts min-1.
After 4 half-life 100 counts min-1.
Age of timber 4 x 5570 22 280 years.
4. A radioisotope used in a laboratory has a half
life of 6.75 hours. It had a count rate of
2000 counts per minute at 8.00 a.m. on Monday.
What would be the count rate at 11 a.m. the
following day?
Between 8.00 a.m. and 11.00 am the next day 27
hours have passed.
Number of half-lives in 27 hours 27/6,75
4
Higher Grade Chemistry
Count rate 2000 ? 1000 ? 500 ? 250 ? 125
counts min-1.