Physics · nuclei · NEET
The parent nucleus loses an alpha particle (2 protons + 2 neutrons). So the atomic number Z goes down by 2 and the mass number A goes down by 4. General rule: X(A,Z) turns into Y(A-4, Z-2) plus an alpha particle. Losing 2 protons means the daughter is a different element, two places to the left in the periodic table.
An alpha particle is a helium-4 nucleus. It carries away 2 protons AND 2 neutrons, so 4 nucleons leave together. That is why A drops by 4. The charge (Z) only counts protons, so Z drops by 2. Do not confuse the two: 4 is total nucleons lost, 2 is protons lost.
The Q-value (also called disintegration energy) is the energy released. Using atomic masses: Q = [m(parent) - m(daughter) - m(helium-4)] times 931.5 MeV per u. If Q is positive, the decay can happen on its own. The energy shows up as kinetic energy shared by the daughter nucleus and the alpha particle.
An alpha particle is a helium-4 NUCLEUS, not a full helium atom. It has no electrons, so it carries a charge of +2e. A neutral helium atom has 2 electrons. When you do Q-value sums using atomic masses, the electron masses cancel out on both sides, so you can safely use the atomic mass of helium-4.
The Q-value energy appears as kinetic energy of the products. By momentum conservation, the heavy daughter nucleus recoils slowly and the light alpha particle carries away most of the kinetic energy. The alpha's share is roughly Q times (A-4)/A, so for heavy nuclei the alpha gets almost all of the energy.
Parent X with mass number A and atomic number Z becomes daughter Y with mass number (A-4) and atomic number (Z-2), plus a helium-4 nucleus (the alpha particle). In symbols: (A,Z)X gives (A-4, Z-2)Y + (4,2)He.
Uranium-238 decays to Thorium-234 by emitting an alpha particle: U-238 (Z=92) gives Th-234 (Z=90) plus He-4. Notice A: 238 = 234 + 4 and Z: 92 = 90 + 2. Its Q-value is about 4.25 MeV.
Take the atomic mass of the parent, subtract the atomic masses of the daughter and of helium-4, then multiply the leftover mass by 931.5 MeV per u. Q = [m(parent) - m(daughter) - m(He-4)] x 931.5 MeV. A positive Q means the decay is allowed.
Heavy nuclei like uranium and radium have too many protons, so the Coulomb repulsion between protons is very large. Emitting an alpha particle removes 2 protons and 2 neutrons at once, making the nucleus more stable. Light nuclei do not gain stability this way, so they rarely undergo alpha decay.
No. By conservation of momentum the daughter nucleus also recoils. But because the daughter is much heavier than the alpha, the alpha takes almost all the kinetic energy. The alpha's kinetic energy is about Q times (A-4)/A, which is close to Q for heavy parents.
An alpha particle is a helium-4 nucleus. It has 2 protons and 2 neutrons, a charge of +2e, and a mass of about 4 u (approximately 6.64 x 10^-27 kg). It has no electrons.
