A sample of rock is found to contain 200 grams of a parent isotope.how many grams of the parent isotope will remain after one half life

Question

asked Feb 13, 2020 43.7k views

2 Answers

Csano · Answer 1 · 2020-02-16T22:01:19+0000

Answer: 100 grams of the parent isotope will remain after one half life.

Step-by-step explanation:

Mass of the isotope present at initial stage =
N_o=200 g

The mass of the parent isotope left after the time ,t=N

Time taken by the samle ,t =
$t_{(1)/(2)}$

The half life of the sample :
$t_{(1)/(2)}$

$N=N_o* e^(-\lambda t)$

$\lambda =\frac{0.693}{t_{(1)/(2)}}$

$\ln[N]=ln[N^o]-\frac{0.693}{t_{(1)/(2)}}* t_{(1)/(2)}$

2=([N_o])/([N])

[N]=(N_o)/(2)=(200 g)/(2)=100 g

100 grams of the parent isotope will remain after one half life.