Question

Radon (Rn) is the heaviest, and only radioactive, member of Group 8A(18) (noble gases). It is a product of the disintegration of heavier radioactive nuclei found in minute concentrations in many common rocks used for building and construction. In recent years, there has been growing concern about the cancers caused from inhaled residential radon. If 1.0X10¹⁵atoms of radium (Ra) produce an average of 1.37X310⁴ atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 1.0 g of Ra?

Answer 1

Given data                Atomic mass of Ra= 226g/mol

no. of moles =1.0/226g/mol           =0.04424moles

no. of atoms in 0.044moles

no. of atoms =no. of moles x avogadro's number

= 0.044x 6.022 x10^23                  = 0.264968 x 10^22

 If 10^15  atoms of Ra produce 1,373*10^4  atoms of Rn per second then 2,66 *10^21  forms 3,658*10^10 atoms of Rn per second.

Day has 246060=86400 s

That means that 2,66x10^21  atoms of Ra produces 3,16 x10^15  atoms of Rn in a day.

N(Rn)=3.16* 10 ^15                           n(Rn)=N/NA

n(Rn)=5,25*10−9                              pV=nR*T

T=273.15K                                        R=8,314

p=101325Pa                                      V=n∗R∗T/p

V=5.25∗10^−9 ∗ 8.314 ∗ 273.15  /  101325

V=1.1810^−10 m^3 =   118 x10^-7 liters of Rn, measured at STP, are produced per day by 1.0 g of Ra

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