Question

Sodium-24, which is used to locate blood clots in the human circulatory system, has a half-life of 15.0 h . A sample of sodium-24 with an inital mass of 13.0 g was stored for 45.0 h . How many grams of sodium-24 are left in the sample after 45.0 h ?

Answer 1

0.3967mg of sodium-24 are left

Step-by-step explanation:

If the half life of radioactive element (which is sodium-24 here) is
`T_(1/2)`, then at the end of this time the number of atoms in the sample will become half i.e. 1/2 .

if the original amount of atoms is N°. The formula for calculating the remaining atoms (N) left in the sample after t half lives would be:

`N=N^(o)  * (1/2)^(t)`

Here, in this question,

Given amount of sodium-24 = N° = 13 grams

Half life of sodium-24 = t = 15

and Remaining amount of sodium after 45 hours = N = ?

Therefore, using the given Forumla:

`N=(13)/(2^(15) )`

`N= 3.967*10^(-4) g\\ N=0.3967 mg`