Respuesta :
Answer:
[tex]5.79\times 10^{6}\ Bq[/tex]
Explanation:
Calculation of the moles of sodium perchlorate as:-
Mass = 54.3 mg
Also, 1 mg = 0.001 g
So, Mass = [tex]0.0543\ g[/tex]
Molar mass of sodium perchlorate = 122.44 g/mol
The formula for the calculation of moles is shown below:
[tex]moles = \frac{Mass\ taken}{Molar\ mass}[/tex]
Thus,
[tex]Moles= \frac{0.0543\ g}{122.44\ g/mol}[/tex]
[tex]Moles= 0.0004435\ mol[/tex]
Also, given that it contains 29.6 % of the radioactive Chlorine
So, Moles of radioactive chlorine in the sample = [tex]\frac{29.6}{100}\times 0.0004435\ mol=0.000131276\ mol[/tex]
1 mole of Chlorine contains [tex]6.023\times 10^{23}[/tex] atoms of chlorine
So,
0.000131276 mole of Chlorine contains [tex]0.000131276\times 6.023\times 10^{23}[/tex] atoms of chlorine
Atoms of radioactive chlorine in the sample = [tex]7.9\times 10^{19}[/tex]
Given that:
Half life = [tex]3.0\times 10^5[/tex] year
1 year = [tex]3.154\times 10^7[/tex] s
Half life = [tex]3.0\times 10^5\times 3.154\times 10^7[/tex] s = 9462000000000 s
The expression for half-life is:-
[tex]t_{1/2}=\frac {ln\ 2}{k}[/tex]
Where, k is rate constant
So,
[tex]k=\frac {ln\ 2}{t_{1/2}}[/tex]
[tex]k=\frac{ln\ 2}{9462000000000}\ s^{-1}[/tex]
The rate constant, k =[tex]7.33\times 10^{-14}[/tex] s⁻¹
Disintegration is:-
Disintegrations per second = Rate constant*Number of atoms = [tex]7.33\times 10^{-14}\times 7.9\times 10^{19}\ Bq[/tex] = [tex]5.79\times 10^{6}\ Bq[/tex]
