Question

Radioactive Decay:

The half life of a
certain radioactive
substance is 46 days.
There are 12.6 g
present initally.

HELP PLS

Answer 1

The question is incomplete, here is the complete question:

The half-life of a certain radioactive substance is 46 days. There are 12.6 g present initially.

When will there be less than 1 g remaining?

Answer: The time required for a radioactive substance to remain less than 1 gram is 168.27 days.

Explanation:

All radioactive decay processes follow first order reaction.

To calculate the rate constant by given half life of the reaction, we use the equation:

`k=(0.693)/(t_(1/2))`

where,

`t_(1/2)` = half life period of the reaction = 46 days

k = rate constant = ?

Putting values in above equation, we get:

`k=(0.693)/(46days)\\\\k=0.01506days^(-1)`

The formula used to calculate the time period for a first order reaction follows:

`t=(2.303)/(k)\log (a)/((a-x))`

where,

k = rate constant =
`0.01506days^(-1)`

t = time period = ? days

a = initial concentration of the reactant = 12.6 g

a - x = concentration of reactant left after time 't' = 1 g

Putting values in above equation, we get:

`t=(2.303)/(0.01506days^(-1))\log (12.6g)/(1g)\\\\t=168.27days`

Hence, the time required for a radioactive substance to remain less than 1 gram is 168.27 days.