Question

what is the value of Z?

Answer 1

^238U_92 is known to undergo radioactive decay to form ^206Pb_82 by emitting alpha and beta particles. A rock initially contained 68 × 10^-6 g of ^238U_92. if the number of alpha particles that it would emit during its radioactive decay of ^238U_92 to ^206Pb_82 in three half lives is Z × 10^18 , then the value of Z.

solution : given mass of Uranium = 68 × 10^-6 g

atomic mass of Uranium = 238 g/mol

so, initial no of moles of U = 68 × 10^-6/238 = x (let)

moles of U decayed in three half lives = (1 - 1/2³)x = 7x/8

decay from U to Pb , each U atom decay and produce 8 alpha particles (as 238 - 206 = 32/4 = 8 alpha particles )

and hence total number of alpha particles emitted out = (7/8)x × 8 × Avogadro's number

= (7/8) × 68 × 10^-6/238 × 8 × 6.023 × 10²³

= 1.204 × 10^18

Therefore the value of Z = 1.204 ≈ 1.2