How long a time t will it take for the 133 54xe to decay so that eventually its activity decreases by a factor of 1024?

This is an incomplete question, here is a complete question.

The radioactive isotope is used in pulmonary respiratory studies to image the blood flow and the air reaching the lungs. The half-life of this isotope is 5 days .

How long a time t will it take for the to decay so that eventually its activity decreases by a factor of 1024?

Express your answer numerically in days.

Answer : The time passed in days is, 50 days

Explanation :

Half-life = 5 days

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = time passed by the sample  = ?

a = initial amount of the reactant  = 1

a - x = amount left after decay process =

Now put all the given values in above equation, we get

Therefore, the time passed in days is, 50 days

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