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 × 10^–27 kg).

Answer 1

(a) Number of atoms of ¹⁴C in 1 mole= 6.023 × 10²³
Since 1 atom of ¹⁴C contains (14 – 6) i.e., 8 neutrons, the number of neutrons in 14 g of ¹⁴C is (6.023 × 10²³) ×8. Or, 14 g of ¹⁴C contains (6.022 × 10²³ × 8) neutrons.
Number of neutrons in 7 mg

6.022*10²³*8*7 mg/1400 mg

= 2.4092 × 10²¹
(b) Mass of one neutron = 1.67493 × 10^–27 kg
Mass of total neutrons in 7 g of ¹⁴C
= (2.4092 × 10²¹) (1.67493 × 10^–27 kg)
= 4.0352 × 10^–6 kg