Atomic weight of Th is 232 and its atomic number is 90. The number of `alpha`- and `beta`-particles which be lost so that an isotope of lead (atomic weight 208 and atomic number 82) is produced is

Options

A. `4 alpha + 6 beta`
B. `6 alpha + 4 beta`
C. `8 alpha + 2 beta`
D. `10 alpha + 2 beta`

Answer

B

Explanation

Let the reaction emits `x alpha`-particles and `y beta`-particle
`._(90)Th^(232) rarr x ._(2)He^(4) + y ._(-1)e^(0) + ._(82)Pb^(208)`
Equating atomic mass number on both sides
`232 = 4x + y (0) + 208`
`:.x = (232 - 208)/(4) = (24)/(4) = 6`
`:. alpha`-particles emitted = 6
Equating atomic number on both sides
`90 = 82 + 6 xx 2 + y (-1)`
`:. y = 94 - 90 = 4`
`:. beta`-particle emitted = 4