`99 %` of a radioactive element will decay between

Options

A. 8 and 9 half lives
B. 7 and 8 half lives
C. 9 and 10 half lives
D. 6 and 7 half lives

Answer

D

Explanation

When 99% material decays , the quantity that is left behind is 1% or `(N)/(N_0) = 1/100`
`because (N)/(N_0) = (1/2)^n` where n is the number of half lives.
`therefore 1/100 = (1/2)^n = " or " 1/2^n`
`therefore 2^n = 100 " we find that " 2^6 = 64 " and "2^7 = 128`
n lies between 6 and 7 .