Question

Element X decays radioactively with a half life of 13 minutes. If there are 110 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 2 grams?

Answer 1

Answer : The time taken by the element to decay to 2 grams is, 75.2 minutes

Explanation:

Half-life = 13 min

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

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

`k=\frac{0.693}{13\text{ min}}`

`k=0.0533\text{ min}^(-1)`

Now we have to calculate the time passed.

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

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

where,

k = rate constant =
`0.0533\text{ min}^(-1)`

t = time passed by the sample = ?

a = initial amount of the reactant = 110 g

a - x = amount left after decay process = 2 g

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

`t=(2.303)/(0.0533)\log(110)/(2)`

`t=75.2\text{ min}`

Therefore, the time taken by the element to decay to 2 grams is, 75.2 minutes