Question

it takes 60 days for 1024 grams of element XY to decay to 32 grams. what is the half life of element XY

Answer 1

The half life of element XY is 12 days

Step-by-step explanation:

Given:

Time taken for 1024 grams to decay into 32 grams = 60 days

To Find:

The half life of element XY = ?

Solution:

The Half life is calculated by

`N = N_0 ((1)/(2))^{\frac{t}{t_{(1)/(2)}}`

`t_{(1)/(2)}` =
`\frac{t}{log_{(1)/(2)}( (N(t))/(N_0))}}`

Substituting the values,

`t_{(1)/(2)}` =
`\frac{60}{log_{(1)/(2)}( (32)/(1024))}}`

`t_{(1)/(2)}` =
`\frac{60}{log_{(1)/(2)}(0.03125)}}`

`t_{(1)/(2)}` =
`(60)/(5)`

`t_{(1)/(2)}` = 12