Nuclei

Using R = R₀A^(1/3) with R₀ = 1.2 fm, find the radius of a nucleus with mass number 64.

Two nuclei have mass numbers in the ratio 1 : 3. What is the ratio of their nuclear densities?

A nucleus has a radius exactly half that of a nucleus with mass number 216. What is the mass number of this smaller nucleus?

Using m_p = 1.00728 u, m_n = 1.00867 u, and the actual mass of a helium-4 nucleus M = 4.00260 u, find its binding energy.

How much energy (in kWh) is released by the complete fission of 2 g of U-235, given 200 MeV is released per fission? (Nₐ = 6.022×10²³, 1 MeV = 1.6×10⁻¹³ J)

A power plant needs to generate 16 kW from nuclear fission, where each fission releases 3.2×10⁻¹¹ J. How many fissions are needed per second?

In a fusion reaction involving 2 kg of fuel, the mass defect is 0.5% of the total mass. How much energy is released? (c² = 9×10¹⁶ m²/s²)

A γ-photon of energy 2.02 MeV undergoes pair production near a nucleus. What is the kinetic energy of each particle produced (assuming the extra energy splits equally)?

²²⁶Ra (mass 226.02540 u) undergoes α-decay to ²²²Rn (mass 222.01757 u), emitting an α-particle (mass 4.00260 u). Find the Q-value of this decay.

A nuclide undergoes β⁺ decay. The atomic mass of the parent exceeds that of the daughter (both already include all their electrons) by 0.00165 u. Find the Q-value. (mₑ = 0.00055 u, 1 u = 931 MeV)

A radioactive substance has decay constant λ = 0.0231 per year. Find its half-life.

What fraction of a radioactive sample remains undecayed after 3 half-lives have elapsed?

A radioactive sample has decayed until only 25% of the original number of nuclei remain. How many half-lives have elapsed?

A radioactive sample has a half-life of 10 days. What is its decay constant?

A radioactive sample has decay constant λ = 0.1 per second. What fraction of the original nuclei remain after 10 seconds?

A nucleus ²³⁴₉₀Th decays through a series of α and β⁻ emissions and ultimately becomes ²¹⁰₈₂Pb. How many α-particles and β⁻-particles are emitted in total?

A nuclear reactor briefly operates with a reproduction factor K slightly greater than 1 during startup. What happens to the rate of the chain reaction?

Fission of U-235 releases about 200 MeV per event; fusion of four hydrogen nuclei into helium releases about 26 MeV per event. Roughly how many times more energy does fusion release per nucleon compared to fission?