Question

The mass of an object changes from $0.2g$ to $0.025g$ in $1500$ years. The half life of the object is:

• A. 500 yrs
• B. 600 yrs
• C. 800 yrs
• D. 950 yrs

Answer 1

Answer: (A)

Given that
Initial value $N_o=0.2gm$.
Final value $(N)=0.025gm$
Time decay $(T)=1500$ yrs.
By using :
$\frac{N}{N_o}={\left(\frac{1}{2}\right)}^n$
$\frac{0.025}{0.2}={\left(\frac{1}{2}\right)}^n$
or $\frac{1}{8}={\left(\frac{1}{2}\right)}^n$
or ${\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^n$
or $n=3$
Now by using
$t_{1/2}=\frac{T}{n}=\frac{1500}{3}$
$=500yrs$