Answer : The parent isotope remain after one half life will be, 100 grams.
Explanation : Given,
Initial mass of the isotope = 200 g
Time taken by the sample, t = \(t_{\frac{1}{2}}\)
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
\(N=N_o\times e^{-(\frac{0.693}{t_{1/2}})\times t_{1/2}}\\\\N=N_o\times e^{-0.693}\)
Now put all the given values in this formula, we get
\(N=200g\times e^{-0.693}\)
\(N=100g\)
Therefore, the parent isotope remain after one half life will be, 100 grams.
