Question

What is the half life if 500 grams decays to 125 grams in 25years?
with steps pls​

Answer 1

Answer: The half life of the sample is 60.26 years.

Step-by-step explanation:

All radioactive decay reactions follow first order reaction.

The formula used to calculate the rate constant for a first order reaction follows:

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

where,

k = rate constant = ?

t = time period = 25 years

a = initial concentration of the reactant = 500 g

a - x = concentration of reactant left after time 't' = (500 - 125) = 375 g

Putting values in above equation, we get:

`k=(2.303)/(25yrs)\log (500g)/(375g)\\\\k=0.0115yr^(-1)`

Now, to calculate the half life period of the reaction, we use the equation:

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

where,

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

k = rate constant =
`0.0115yr^(-1)`

Putting values in above equation, we get:

`t_(1/2)=(0.693)/(0.0115yr^(-1))\\\\t_(1/2)=60.26yrs`

Hence, the half life of the sample is 60.26 years.