The fraction of atoms of radioactive element that decays in 6 days is 7/8. the fraction that decays in 10 days will be

Options

A. 77/80
B. 71/80
C. 31/32
D. 15/16

Answer

C

Explanation

Let number of `alpha` particles decayed be x and number of `beta` particles decayed by y.
Then, equation for the decay is given by
`""_(92)U^(235) to X alpha_(2)^(4) +ybeta_(-1)^(0)+Pb_(82)^(203)`
Equating atomic number of both sides
`235=4x+203` . . (i)
Equating atomic number on both sides
`92=2x-y+82` . . (ii)
Solving Eqs. (i) and (ii), we get
`x=8,y=6`
`therefore8alpha` particles and `6beta` particles are emitted in disintegration.