Answer :
1. 200/2=100. 100/2=50. 50/2=25. So that's 3 to get to 25.
2. 11.46/3=3.82
The answer is (2).
2. 11.46/3=3.82
The answer is (2).
Answer : The correct option is, (2) 3.82 d
Solution : Given,
As we know that the radioactive decays follow first order kinetics.
So, the expression for rate law for first order kinetics is given by :
[tex]k=\frac{2.303}{t}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = time taken for decay process = 11.46 days
a = initial amount of the reactant = 200 g
a - x = amount left after decay process = 25 g
Putting values in above equation, we get the value of rate constant.
[tex]k=\frac{2.303}{11.46}\log\frac{200}{25}=0.1814[/tex]
Now we have to calculate the half life of a radioisotope.
Formula used : [tex]t_{1/2}=\frac{0.693}{k}[/tex]
Putting value of 'k' in this formula, we get the half life.
[tex]t_{1/2}=\frac{0.693}{0.1814}=3.820[/tex]
Therefore, the half-life of a radioisotope is, 3.820 d
