Answer:
The half life of the radioisotope is 12 hours.
Explanation:
Initial mass of the radioisotope = x
Final mass of the radioisotope = \(\frac{1}{16}\times x\) = 0.0625x
Half life of the radioisotope =\(t_{\frac{1}{2}}\)
Age of the radioisotope = t = 48 hours
Formula used :
\(N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}\)
where,
\(N_o\) = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
\(t_{\frac{1}{2}}\) = half life of the isotope
\(\lambda\) = rate constant
\(N=N_o\times e^{-(\frac{0.693}{t_{1/2}})\times t}\)
Now put all the given values in this formula, we get
\(0.0625x=x\times e^{-(\frac{0.693}{t_{1/2}})\times 48 h}\)
\(\ln(0.0625) \times \frac{1}{(-0.693\times 48 h)}=\frac{1}{t_{1/2}}\)
\(t_{1/2} = 11.99 hours = 12 hours\)
The half life of the radioisotope is 12 hours.
