Polonium-210, 210Po, decays to lead-206, 206Pb, by alpha emission according to the equation

210 206 4

84 Po > 82Pb + 2 He

If the half-life, t1/2, of 210Po is 138.4 days, calculate the mass of 206Pb that can be produced from a 565.0-mg sample of polonium(IV) chloride, PoCl4, that is left untouched for 334.7 days. Assume that the only polonium isotope present in the sample is the 210Po isotope. The isotopic molar masses of 210Po is 209.98 g/mol and 206Pb is 205.97 g/mol.

269.9 mg of Lead (Pb-206)  are formed from a sample of 565 mg of PoCl4 after 334.7 days.

Explanation:

From the given data

Half life of Po =t_{1/2}= 138.4 days

The value of K is given as

Here,

Mass of PoCl4 =m_{PoCl4}= 565 mg

The moles of PoCl4 are given as

so initial concentration of Po = N_o=n=0.00161 moles  

Time = t=334.7 days

K = 0.005 day^-1

Putting in first order rate equation

So the total moles after 334.7 days have passed is given as 0.000302.

The moles of Pb formed are given as

And the mass is given as

So 269.9 mg of Lead (Pb-206)  are formed from a sample of 565 mg of PoCl4 after 334.7 days.

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