A radioactive nucleus of uranium-235 (mU = 235 u) decays spontaneously to thorium-231
by emitting an alpha particle (nucleus of a helium atom, symbolised α). The α particle
(mα = 4.00 u) has kinetic energy 4.60 MeV. What is the kinetic energy of the thorium-231
nucleus (mT h = 231 u)?
To find the kinetic energy of the thorium-231 nucleus, we can use the principle of conservation of energy. The total energy of the system should remain constant before and after the alpha decay.
The initial total energy is the sum of the kinetic energy of the alpha particle and the binding energy of the uranium-235 nucleus.
1. Find the binding energy of the uranium-235 (mU = 235 u) nucleus using a nuclear binding energy chart or formula. Let's say the binding energy is E_bind(U) = X MeV.
2. The initial total energy (E_initial) is the sum of the kinetic energy of the alpha particle (E_kin(α)) and the binding energy (E_bind(U)) of the uranium-235 nucleus:
E_initial = E_kin(α) + E_bind(U)
3. We are given the kinetic energy of the alpha particle (E_kin(α)) as 4.60 MeV.
4. Subtract the kinetic energy of the alpha particle from the initial total energy to find the binding energy of the uranium-235 nucleus:
E_bind(U) = E_initial - E_kin(α)
5. The final total energy (E_final) is the sum of the kinetic energy of the thorium-231 (mT h = 231 u) nucleus (E_kin(T h)) and the binding energy of the thorium-231 nucleus (E_bind(T h)).
6. The kinetic energy of the thorium-231 nucleus can be calculated by subtracting the binding energy of the thorium-231 nucleus from the final total energy:
E_kin(T h) = E_final - E_bind(T h)
Therefore, the kinetic energy of the thorium-231 nucleus can be found by calculating E_kin(T h) using the steps described above.