Answer 1

1. A radioactive transformation in which an α-particle is emitted is called α-decay.
   In an α-decay, the atomic number of the nucleus decreases by 2 and the mass number decreases by 4.
   Example: \[\ce{_92^238U->_90^234Th + _2^4\alpha}\]
   Q = [m_U - m_Th - m_α]c²
2. A radioactive transformation in which a β-particle is emitted is called β-decay.
   In a  β^- -decay, the atomic number of the nucleus increases by 1 and the mass number remains unchanged.
   Example: \[\ce{_90^234Th->_91^234Pa + _-1^0e +\bar{v}_e}\]
   where `bar"v"_"e"` is the antineutrino emitted to conserve the momentum, energy and spin.
   Q = [m_Th - m_pa - m_e]c²
   In a β⁺ -decay, the atomic number of the nucleus decreases by 1 and the mass number remains unchanged.
   Example: \[\ce{_15^30P->_14^30Si +_+1^0e +v_e}\]
   where v_e is the neutrino emitted to conserve the momentum, energy and spin.
   Q = [m_P - m_Si - m_e]c² 
3. A given nucleus does not emit α- and -β particles simultaneously. However, on emission of α or β-particles, most nuclei are left in an excited state. A nucleus in an excited state emits a γ-ray photon in a transition to the lower energy state. Hence, α- and β-particle emissions are often accompanied by γ-rays.

\[\ce{_Z^AX->_2^4\alpha{ +} _{Z-2}^{A-4}Y + energy released}\]

\[\ce{_Z^AX->_-1^0\beta{ +} _{Z+1}^{A}Y + energy released}\]

\[\ce{_Z^AX->_0^0\gamma{ +} _{Z}^{A}X}\] (Energy released is carried by the γ-ray photon).