Ten Examples | Problems involving carbon-14 | |

Probs 1-10 | Problems involving uranium-238 | |

Probs 26-40 | Examples and Problems only (no solutions) | Return to Radioactivity menu |

**Problem #11:** The half life of iodine-131 is 8.040 days. What percentage of an iodine-131 sample will remain after 40.20 days?

**Solution:**

40.20 d / 8.040 d = 5(1/2)

^{5}= 0.03125percent remaining = 3.125%

**Problem #12:** The half-life of thorium-227 is 18.72 days How many days are required for three-fourths of a given amount to decay?

**Solution:**

3/4 = 0.75 <--- amount decayed1 − 0.75 = 0.25 <--- amount remaining

(1/2)

^{n}= 0.25n = 2

(18.72 day) (2) = 37.44 day

**Problem #13:** If you start with 5.32 x 10^{9} atoms of Cs-137, how much time will pass before the amount remaining is 5.20 x 10^{6} atoms? The half-life of Cs-137 is 30.17 years.

**Solution:**

5.20 x 10^{6}/ 5.32 x 10^{9}= 0.0009774436 (the decimal amount remaining)(1/2)

^{n}= 0.0009774436n log 0.5 = log 0.0009774436

n = 9.99869892 half-lives

(30.17 yr) (10) = 301.7 yr

**Problem #14:** The half-life of the radioactive isotope phosphorus-32 is 14.3 days. How long until a sample loses 99% of its radioactivity?

**Solution:**

99% loss means 1% remaining1% = 0.01

(1/2)

^{n}= 0.01n log 0.5 = log 0.01

n = 6.643856

(14.3 day) (6.643856) = 95.0 day

**Problem #15:** The half-life of palladium-100 is 4 days. After 12 days a sample of Pd-100 has been reduced to a mass of 4.00 mg. (a) Determine the starting mass. (b) What is the mass 8 weeks after the start?

**Solution:**

12 day / 4 day = 3(1/2)

^{3}= 0.1254.00 mg / 0.125 = 32.0 mg

8 weeks = 56 days

56 d / 4 = 14 half-lives

(1/2)

^{14}= 0.000061035(32.0 mg) (0.000061035) = 0.00195 mg (rounded to three figs)

**Problem #16:** Rn-222 has a half-life of 3.82 days. How long before only 1/16 of the original sample remains?

**Solution:**

recognize 1/16 as a fraction associated with 4 half-lives (from 1/2^{4}= 1/16)3.82 days x 4 = 15.3 days

**Problem #17:** One-eighth of a radioactive sample remains 9 days after it was brought into the lab. What is the half-life?

**Solution:**

One-eighth is evocative of three half-lives.9 day / 3 = 3 day

**Problem #18:** A sample of Se-83 registers 10^{12} disintegrations per second when first tested. What rate would you predict for this sample 3.5 hours later, if the half-life is 22.3 minutes?

**Solution:**

210 min / 22.3 min = 9.42 half-lives (210 min is 3.5 hours)(1/2)

^{9.42}= 0.00146 (the decimal fraction remaining)10

^{12}x 0.00146 = 1.46 x 10^{9}disintegrations per second remaining

**Problem #19:** Iodine-131 has a half-life of 8.040 days. If we start with a 40.0 gram sample, how much will remain after 24.0 days?

**Solution:**

24.0 days / 8.040 days = 2.985 half-lives(1/2)

^{2.985}= 0.1263 (the decimal fraction remaining)40.0 g x 0.1263 = 5.05 g

**Problem #20:** If you start with 2.97 x 10^{22} atoms of molybdenum-99 (half-life = 65.94 hours), how many atoms will remain after one week?

**Solution:**

one week = 168 hours168 / 65.94 = 2.548

(1/2)

^{2.548}= 0.171 (the decimal fraction remaining)(2.97 x 10

^{22}) x 0.171 = 5.08 x 10^{21}

**Problem #21:** The isotope H-3 has a half life of 12.26 years. Find the fraction remaining after 49 years.

**Solution:**

49 / 12.26 = 3.9967(1/2)

^{3.9967}= 0.0626

**Problem #22:** How long will it take for a 64.0 g sample of Rn-222 (half-life = 3.8235 days) to decay to 8.00 g?

**Solution:**

8.00 / 64.0 = 0.125 (the decimal fraction remaining)(1/2)

^{n}= 0.125by experience, n = 3 (remember that 0.125 is 1/8)

3.8235 x 3 = 11.4705 days

**Problem #23:** A scientist needs 10.0 micrograms of Ca-47 (half-life = 4.50 days) to do an experiment on an animal. If the delivery time is 50.0 hours, how many micrograms of ^{47}CaCO_{3} must the scientist order?

**Solution:**

4.50 days x 24 hrs/day = 108 hrs50/108 = 0.463 half-lives

(1/2)

^{0.463}= 0.725 (the decimal portion of Ca-47 remaining after 50 hrs)10.0 mg / 0.725 = 13.8 mg

**Problem #24:** What precentage of the parent isotope remains after 0.5 half lives have passed?

**Solution:**

(1/2)^{n}= decimal amount remainingwhere n = the number of half-lives

(1/2)

^{0.5}= 0.707The question asks for a percentage, so 70.7%

**Problem #25:** Manganese-56 has a half-life of 2.6 h. What is the mass of manganese-56 in a 1.0 g sample of the isotope at the end of 10.4 h?

**Solution:**

10.4 / 2.6 = 44 half-lives = 0.0625 remaining

0.0625 g

Ten Examples | Problems involving carbon-14 | |

Probs 1-10 | Problems involving uranium-238 | |

Probs 26-40 | Examples and Problems only (no solutions) | Return to Radioactivity menu |