Answer: 43.73 seconds
Explanation:
Half-life of indium = 14.10 sec
First we have to calculate the rate constant, we use the formula :


Now we have to calculate the age of the sample:
Expression for rate law for first order kinetics is given by:

where,
k = rate constant
t = age of sample = ?
a = initial amount of the reactant = 7.70 mg=

a - x = amount left after decay process = 
Now put all the given values in above equation, we get


Thus it would take 43.73 seconds sample to decay from 7.70 mg to 900 µg.