A radioactive element ₉₂²⁴²X emits two α-particles, one electron and two positrons. The product nucleus is represented by _P²³⁴Y. The value of P is __________.

Solution

Physics sir · 3 steps

Track only the charge: each emission shifts Z by a fixed amount, so add them up one by one.

1. Charge change rules. An α-particle carries away 2 protons, so Z drops by 2. Emitting an electron (β⁻) turns a neutron into a proton, so Z rises by 1. Emitting a positron (β⁺) turns a proton into a neutron, so Z drops by 1.

   Emission	Change in Z	Change in A
   Two α-particles	2 × (-2) = -4	2 × (-4) = -8
   One electron	+1	0
   Two positrons	2 × (-1) = -2	0

2. Check the mass number. Only the α-particles change A: 242 - 8 = 234, which matches the product. So the bookkeeping is consistent.

   P = 92 - 4 + 1 - 2 = 87

3. So. The atomic number of the product Y is 87.

The common slip: 85. Treating the emitted electron like a positron, as lowering Z by 1, gives 92 - 4 - 1 - 2 = 85 instead of 87.

The idea to keep. Alpha lowers Z by 2 and A by 4. An electron raises Z by 1, a positron lowers Z by 1, and neither changes A. Balance charge and mass separately.

Answer from the NTA final answer key. Solution by PrepWiser.