Question

After decaying for 48 hours, one-sixteenth (1/16) of the original mass of a radioisotope sample remains unchanged. What is the half-life of this radioisotope?

Answer 1

The half-life of this radioisotope : 12 hr

Further explanation

The atomic nucleus can experience decay into 2 particles or more due to the instability of its atomic nucleus.  

Usually radioactive elements have an unstable atomic nucleus.  

General formulas used in decay:  

$\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{t/t\frac{1}{2} }}}$

t = duration of decay  

t 1/2 = half-life  

N₀ = the number of initial radioactive atoms  

Nt = the number of radioactive atoms left after decaying during T time  

t=48 hr

$\tt \dfrac{Nt}{No}=\dfrac{1}{16}$

The half-life :

$\tt \dfrac{1}{16}=\dfrac{1}{2}^{(48/t\frac{1}{2} )}\\\\(\dfrac{1}{2})^4=(\dfrac{1}{2})^{48/t\frac{1}{2}}\\\\4=48/t\frac{1}{2}\\\\t\frac{1}{2}=12~hr$