Question

Calculate the time required to decay a 15/16 of the radioactive element if half life of the element is 1600 years.

• A. 1000 years
• B. 1500 years
• C. 1600 years
• D. 3200 years
• E. 6400 years

Answer 1

Answer: (E)

6400 years

Let the initial amount of radioactive element $=N_0$

The remaining amount after decay at time t is $N=N_0-N_0\left(15/16\right)=N_0/16$

From law of radio activity, $N=N_0{e}^{-\lambda t}$ where decay constant, $\lambda =ln2/t_{1/2}=ln2/1600$

So, $e^{\lambda t}=N_0/N=16$

Take ln from sides, $\lambda t=ln16=4ln2$

or $t=\frac{4ln2}{ln2/1600}=6400$ years