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

(Assume that mass of a neutron = 1.675 × 10 ^{ –27 } kg).

The molar mass of ^{14}C is 14g. Therefore we will first calculate the number of moles in 7mg (or 0.007 g) of ^{14}C.

Number of moles in 0.007 g of ^{14}C = mass / molar mass

= 0.007 / 14 = 0.0005 moles

Now 1 mole of ^{14}C = 6.023 X 10^{23} atoms of ^{14}C

Therefore 0.0005 moles of ^{14}C = 0.0005 X 6.023 X 10^{23} atoms of ^{14}C

= 3.015 X 10^{20} atoms of ^{14}C

Now 1 atom of ^{14}C contains 6 protons (atomic number of Carbon is 7).

Therefore there are 8 neutrons present in 1 atom of ^{14}C.

Thus 1 atom of ^{14}C = 8 neutrons

Therefore

3.015 X 10^{20} atoms of ^{14}C = 8 X 3.015 X 10^{20} neutrons of ^{14}C

= 2.412 X 10^{21} neutrons of ^{14}C

Now mass of 1 neutrons = 1.675 X 10^{-27} Kg

Therefore mass of 2.412 X 10^{21} neutrons of ^{14}C = 2.412 X 10^{21} X 1.675 X 10^{-27} Kg

= 4.04 X 10^{-6} Kg

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