Nuclear Physics — Numerical Practice
Covers: nuclide notation (neutrons = A − Z), half-life calculations, decay equation balancing, and background radiation correction. 16 questions.
A. Nuclide Notation
For the nuclide with A = 23 and Z = 11 (sodium-23), calculate the number of protons, neutrons, and electrons.
For the nuclide with A = 40 and Z = 18 (argon-40), calculate the number of neutrons.
An isotope has 6 protons and 8 neutrons. Calculate its nucleon number.
Two isotopes of the same element have nucleon numbers 35 and 37, both with 17 protons. Calculate the number of neutrons in each.
An atom has 92 protons and a nucleon number of 238. Calculate the number of neutrons.
B. Half-Life Calculations
A sample has an initial activity of 640 counts/min and a half-life of 5 days. Calculate its activity after 20 days.
A sample’s activity falls from 800 counts/min to 100 counts/min over 45 minutes. Calculate the half-life.
A sample has a half-life of 8 years and an initial activity of 2000 Bq. Calculate its activity after 24 years.
A sample’s activity drops to one-eighth of its original value after 60 minutes. Calculate its half-life.
A sample’s activity is 50 counts/min after 3 half-lives have passed. Calculate its original activity.
Explain why an isotope with a very long half-life is unsuitable for use as a medical tracer injected into a patient.
C. Decay Equations and Background Correction
A measured count rate is 95 counts/min, and the background count rate is 15 counts/min. Calculate the corrected count rate.
A corrected count rate is 120 counts/min, and the measured count rate (with the source present) was 138 counts/min. Calculate the background count rate.
Radium-226 (Z = 88) decays by alpha emission to form radon (Z = 86). Write the balanced decay equation, and check that both the nucleon number and proton number balance.
Carbon-14 (Z = 6) decays by beta emission to form nitrogen (Z = 7). Write the balanced decay equation.
Explain why the nucleon number does not change during beta decay, even though the proton number does.
Mastery Test
A nuclide has A = 27 and Z = 13. Calculate the number of neutrons.
An isotope has 8 protons and 10 neutrons. Calculate its nucleon number.
A sample has an activity of 500 counts/min and a half-life of 10 minutes. Calculate its activity after 30 minutes.
A sample’s activity falls from 1000 counts/min to 125 counts/min over 90 minutes. Calculate the half-life.
A measured count rate is 110 counts/min, and the background count rate is 20 counts/min. Calculate the corrected count rate.
Explain why alpha particles have a very short range when travelling through air.
Uranium-238 (Z = 92) decays by alpha emission to form thorium (Z = 90). Write the balanced decay equation.
Explain what is meant by radioactive decay being “spontaneous and random.”
A sample’s activity is 30 counts/min after 4 half-lives have passed. Calculate its original activity.
State one precaution that should be taken when handling a radioactive source.
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