Question

The half-life of na-24 is 15 hours . when there are 1000 atoms of na-24 in a sample , a scientist starts a stopwatch . the scientist stops the stopwatch at 45 hours , there are atoms of na-24 remaining

Answer 1

125 Each half life it divides by 2 the amount
1000/2=500
500/2=250
250/2=125

Answer 2

Answer : The atoms of Na-24 remaining are, 125.1 atoms

Explanation :

Half-life = 15 hours

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

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

`k=\frac{0.693}{15\text{ hours}}`

`k=4.62* 10^(-2)\text{ hours}^(-1)`

Now we have to calculate the left atoms of Na-24.

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

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

where,

k = rate constant =
`4.62* 10^(-2)\text{ hours}^(-1)`

t = time passed by the sample = 45 hours

a = initial atoms of the reactant = 1000

a - x = atoms left after decay process = ?

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

`45=(2.303)/(4.62* 10^(-2))\log(1000)/(a-x)`

`a-x=125.1atoms`

Therefore, the atoms of Na-24 remaining are, 125.1 atoms