Answer :
100g of isotope, as one half of the isotope will be lost every half life (hence the name).
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 = [tex]t_{\frac{1}{2}}[/tex]
Formula used :
[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]N_o[/tex] = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope
[tex]\lambda[/tex] = rate constant
[tex]N=N_o\times e^{-(\frac{0.693}{t_{1/2}})\times t_{1/2}}\\\\N=N_o\times e^{-0.693}[/tex]
Now put all the given values in this formula, we get
[tex]N=200g\times e^{-0.693}[/tex]
[tex]N=100g[/tex]
Therefore, the parent isotope remain after one half life will be, 100 grams.