Question

Find (i) the total number of neutrons and (ii) the total mass of neutrons in $7mg$ of ${}^{14}C$

[Assuming that mass of neutron $=$ mass of hydrogen atom].

Answer 1

Number of atoms of $C^{14}$ in 1 mole $=6.023\times {10}^{23}$

Since 1 atom of $C^{14}$contains (14 – 6) i.e., 8 neutrons, the number of neutrons in 14 g of $C^{14}$ is $(6.023\times {10}^{23})\times 8$. Or, 14 g of $C^{14}$ contains $(6.022\times {10}^{23}\times 8)$ neutrons.

Number of neutrons in 7 mg

$=2.4092\times {10}^{21}$

(b) Mass of one neutron $=1.67493\times {10}^{–27}$ kg

Mass of total neutrons in 7 g of $C^{14}$

$=(2.4092\times {10}^{21})(1.67493\times {10}^{–27}kg)$

$=4.0352\times {10}^{–6}kg$