Quick answer: Atoms have discrete energy levels, so they emit and absorb photons of fixed energy equal to the gap between levels. This AP Physics 2 worksheet on nuclear decay gives 20 problems from easy to hard: counting protons and neutrons, hydrogen energy levels and a visible hydrogen line. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These problems train you to calculate photon energies from energy levels, balance nuclear equations, apply half-lives and convert mass defects into energy. They climb from simple recall to AP-style multi-step reasoning and data analysis. They suit AP Physics 2 unit 15 and the modern physics sections of A level courses.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 15
Problem 1 Counting protons and neutrons ★★★
Count the particles in two nuclei.1. How many protons and neutrons are in ¹⁴₆C?
2. How many protons and neutrons are in ²³⁵₉₂U?
Problem 2 Hydrogen energy levels ★★★
Use E = −13.6 eV / n².1. Calculate the energies for n = 1, 2, 3 and 4.
2. Calculate the energy needed to remove an electron from n = 2.
Problem 3 A visible hydrogen line ★★★
Aarav in Pune studies the diagram of hydrogen levels.1. Calculate the energy of the photon emitted in the transition n = 4 to n = 2.
2. Calculate its wavelength using hc = 1240 eV·nm.
Problem 4 Absorbing a photon ★★★
A hydrogen atom is in its ground state (n = 1).1. Calculate the energy needed to excite it to n = 2.
2. State whether it can absorb a photon of 11.0 eV, and explain.
Problem 5 Alpha decay equation ★★★
Radium-226 (Z = 88) undergoes alpha decay to radon.1. Write the nuclear equation.
2. State the mass number and atomic number of the daughter nucleus.
Problem 6 Beta decay equation ★★★
Cobalt-60 (Z = 27) decays by beta minus emission.1. Write the nuclear equation.
2. State the atomic number of the daughter.
Problem 7 Counting half-lives ★★★
Chiamaka in Lagos has 64 g of an isotope with half-life 5.0 days.1. Calculate the mass left after 15 days.
2. Calculate the mass left after 20 days.
3. State the fraction left after 15 days.
Problem 8 Reading a decay graph ★★★
A student records the count rate from a sample.1. Read the half-life.
2. Predict the count rate at 30 hours.
3. Explain why the rate never reaches exactly zero.
Problem 9 Mass to energy ★★★
Diego in Texas imagines converting 1.0 g of matter completely to energy.1. Calculate the energy released using c = 3.00 × 10⁸ m/s.
2. Compare it with the energy of 1 tonne of TNT, which is 4.2 × 10⁹ J.
Problem 10 Unit conversion for mass defect ★★★
A nuclear reaction loses a mass of 0.0050 u. Use 1 u = 931.5 MeV/c² and 1 MeV = 1.60 × 10⁻¹³ J.1. Calculate the energy released in MeV.
2. Convert the answer to joules.
Problem 11 Identify the radiation ★★★
Kofi in Accra measures the net count rate of a source with different absorbers between the source and a detector.| Absorber | none | paper | 3 mm aluminium | 5 cm lead |
|---|---|---|---|---|
| Net counts per minute | 1200 | 1190 | 400 | 5 |
1. Decide which radiations are emitted.
2. Estimate the fraction of the count rate due to each.
Problem 12 Carbon dating ★★★
Carbon-14 has a half-life of 5730 years. A bone has less carbon-14 than living tissue.1. Calculate the age if 12.5 % of the original carbon-14 remains.
2. Estimate the age range if 30 % remains.
3. Calculate the age for 30 % using logarithms.
Problem 13 Why spectra are lines ★★★
Hot hydrogen gas gives a spectrum of bright lines, but a hot filament gives a continuous rainbow.1. Explain why the gas gives lines.
2. Explain why a cool gas placed in front of the filament produces dark lines.
Problem 14 Lyman and Balmer lines ★★★
Compare the transitions n = 2 to n = 1 and n = 3 to n = 2 in hydrogen. Use hc = 1240 eV·nm.1. Calculate the energy of each photon.
2. Calculate the wavelength of each.
3. State the region of the spectrum for each.
Problem 15 Binding energy of the deuteron ★★★
Use proton 1.007276 u, neutron 1.008665 u and deuteron 2.013553 u, with 1 u = 931.5 MeV.1. Calculate the mass defect.
2. Calculate the binding energy.
3. Calculate the binding energy per nucleon.
Problem 16 Energy from radium decay ★★★
Radium-226 (226.025410 u) decays to radon-222 (222.017578 u) by emitting an alpha particle (4.002603 u). Use 1 u = 931.5 MeV.1. Calculate the mass lost in the decay.
2. Calculate the energy released.
3. Estimate the kinetic energy of the alpha particle, given that momentum is shared so that K is inversely proportional to mass.
Problem 17 Activity of a medical tracer ★★★
A hospital sample holds 2.0 × 10¹⁰ nuclei of technetium-99m, half-life 6.0 h. Use A = (ln 2 / T)N.1. Convert the half-life to seconds.
2. Calculate the initial activity in becquerel.
3. Calculate the activity after 18 hours.
Problem 18 Power of the Sun ★★★
In the Sun, four hydrogen atoms (1.007825 u each) fuse into one helium-4 atom (4.002603 u). The Sun radiates 3.8 × 10²⁶ W. Use 1 u = 931.5 MeV and c = 3.00 × 10⁸ m/s.1. Calculate the mass lost in one fusion sequence.
2. Calculate the energy released in MeV.
3. Calculate the mass the Sun converts to energy each second.
Problem 19 Lines from a hypothetical atom ★★★
A hypothetical atom has the energy levels shown. Use hc = 1240 eV·nm.1. State how many different emission lines are possible from n = 4.
2. Calculate the longest wavelength emitted and state its region.
3. Calculate the shortest wavelength emitted.
Problem 20 Half-life from lab data ★★★
A short-lived isotope gives these corrected counts per 10 s in a Geiger counter.| t (min) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| counts | 480 | 364 | 276 | 209 | 158 | 120 |
1. Plot or inspect the data and estimate the half-life.
2. Check your value using the counts at 0 min and 5 min.
3. Explain why background counts must be subtracted first.
