Question

A 300 gram radioactive sample has half life of 3 hour's. After 18 hour's remaining quantity will be:

• A. $4.68\ gram$
• B. $2.34\ gram$
• C. $3.34\ gram$
• D. $9.37\ gram$

Answer 1

Answer: (A)

$4.68\ gram$

Answer 2

The radioactive decay of a substance can be modeled using the formula:

$N(t)=N_0​(\frac 12​)^{\frac tT}$​

Where:

• $N(t)$ is the amount of the substance at time t.
• $N_0​$ is the initial amount of the substance.
• $T$ is the half-life of the substance.

In this case, we have:

• $N_0$ ​= 300 grams (initial amount)
• T = 3 hours (half-life)
• t = 18 hours (time elapsed)

$N(18)$ = $300(\frac 12​)^{\frac {18​}{3}}$

$N(18)$ = $300(\frac 12)^6$

$N(18)$ = $300(\frac {1}{64})$

$N(18)$ = $4.6875$

The remaining quantity after 18 hours is approximately 4.6875 grams.

So, the correct option is (A): $4.68\ gram$