Question

$90$% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initial sample will decay in a total time $2t$?

• A. $20$%
• B. $19$%
• C. $40$%
• D. $38$%

Answer 1

Answer: (B)

$19$%

Given that $90$% is left un-decayed after time '$t$'.
Hence, $10$% decays in time '$t$'.
Initially assume that the amount of substance is '$x$'
After time '$t$' $10$% is decayed.
i.e. Amount of substance left $=0.9x$
After further time '$t$' another $10$% is decayed.

i.e. $0.1\times 0.9x$ is decayed
Leaving behind $0.81x$.
Hence after time $2t$ we see that $0.19x$ has decayed, which is $19$%.