Question

If isotope distribution of c12 and c14 id 98% and 2% respectively then the number of c12atoms in 14g of carbon is

a.3.011*10^23

b.6.885*10^23

Answer 1

Weight of Carbon = 14g
molecular weight of C¹² = 12g/mol
∴ number of mole = 14g/12g/mol = 7/6 mol
Number of carbon atoms = mole × Avogadro's number
= 7/6 × 6.023 × 10²³
= 7.026 × 10²³

∵ occurrence of C¹² = 98 %
So, number of C¹² atoms = 7.026 × 10²³ × 98/100
= 6.886 × 10²³
Hence, number of C¹² atoms = 6.886 × 10²³ .
So,. option (b) is correct.

Answer 2

Solution :

14 g of carbon 14 atom contains =6.023×1023atoms=6.023×1023atoms

1 g of carbon 14 atom contains =6.023×1023/14=6.023×1023/14

12 g of carbon 14 atom contains =(6.023×1023×12)/14=(6.023×1023×12)/14

=5.16×1023=5.16×1023

Now its 2%2% is (5.16×1023×2)/100(5.16×1023×2)/100

=10.32×1021=10.32×1021

So, the number of C−14C−14 atoms in 12 g of carbon is 10.32×1021