The total mass of neutrons in 7 mg $C^{14}$ of (assume mass of a neutron = $1.675\times {10}^{-27}$ ) is

1 mole of C – 14= 14 g =  $6.022\times {10}^{23}$ carbon atoms Numbers of neutrons 1 carbon atom = mass number – atomic number = $\text{14 }-\text{ 6 }=\text{ 8}$ neutrons

$6.023\times {10}^{23}$carbon atoms will contain $6.023\times {10}^{23}\times 8$ neutrons

$\therefore 14gC-14have6.023\times {10}^{23}\times 8neutrons$

Hence, $=7\times {10}^{-3}gC-14willhave$

 $=\frac{7\times {10}^{-3}\times 6.023\times {10}^{23}\times 8}{14}neutrons$

$=24.092\times {10}^{20}neutrons$

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

$Massof1neutron=1.675\times {10}^{-27}kg$

$\therefore Massof2.4092\times {10}^{21}neutrons$

$=2.4092\times {10}^{21}\times 1.675\times {10}^{-27}kg$

$=4.0354\times {10}^{-6}kg$