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 :

$k=\frac{0.693}{t_{1/2}}$

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

$k=4.62\times 10^{-2}\text{ hours}^{-1}$

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

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

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  = $4.62\times 10^{-2}\text{ hours}^{-1}$

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

$45=\frac{2.303}{4.62\times 10^{-2}}\log\frac{1000}{a-x}$

$a-x=125.1atoms$

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