Question

Find (a) the total number and (b) the total mass of neutrons in 7 mg of ¹⁴C.

[Assume that mass of a neutron = 1.675 x 10^-27 kg]

Answer 1

Mass of ¹⁴C = 7 mg = 7 x 10^-3 g

Molar mass of ¹⁴C = 14 g/mol

Therefore, amount of ¹⁴C in 7 mg sample

= {7 x 10^-3 g}/{14 g/mol} = 5 x 10^-4 mol

Each carbon - 14 nucleus contains 8 neutrons, hence

(a) No. of neutrons in 7 mg sample of ¹⁴C

= 8 x 5 x 10^-4 mol x 6.023 x 10²³ mol^-1

= 2.4088 x 10²¹

(b) Total mass of neutrons in 7 mg sample of ¹⁴C

= 2.41 x 10²¹ x 1.675 x 10^-27 kg

= 4.0347 x 10^-6 kg