A radioactive element $$^{242}_{92}$$X emits two $$\alpha$$-particles, one electron and two positrons. The product nucleus is represented by $$^{234}_{P}$$Y. The value of $$P$$ is ______.

We are given the radioactive element $$^{242}_{92}$$X which emits two $$\alpha$$-particles, one electron ($$\beta^-$$), and two positrons ($$\beta^+$$). The product nucleus is $$^{234}_{P}$$Y.

Effect of each emission on mass number (A) and atomic number (Z):

Each $$\alpha$$-particle ($$^4_2$$He): $$A$$ decreases by 4, $$Z$$ decreases by 2.

Each $$\beta^-$$ (electron): $$A$$ unchanged, $$Z$$ increases by 1 (neutron converts to proton).

Each $$\beta^+$$ (positron): $$A$$ unchanged, $$Z$$ decreases by 1 (proton converts to neutron).

Mass number of product:

$$A_Y = 242 - 2 \times 4 = 242 - 8 = 234 \checkmark$$

Atomic number of product:

$$P = 92 - 2(2) + 1(1) - 2(1) = 92 - 4 + 1 - 2 = 87$$

The value of $$P$$ is $$\boxed{87}$$.