Question

find 1. the total no. of neutrons 2. the total mass of neutron in 7mg of C14

Answer 1

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

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

= 0.007 / 14 = 0.0005 moles

Now 1 mole of 14C = 6.023 X 1023 atoms of 14C

Therefore 0.0005 moles of 14C = 0.0005 X 6.023 X 1023 atoms of 14C

= 3.015 X 1020 atoms of 14C

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

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

Thus 1 atom of 14C = 8 neutrons

Therefore

3.015 X 1020 atoms of 14C = 8 X 3.015 X 1020 neutrons of 14C

= 2.412 X 1021 neutrons of 14C

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

Therefore mass of 2.412 X 1021 neutrons of 14C = 2.412 X 1021 X 1.675 X 10-27 Kg

= 4.04 X 10-6 Kg



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Answer 2

Answer:

Here we have 14C i.e Carbon with mass number = 14

Therefore No of protons + noi of neutrons = 14

Now Atomic no of carbon = No of protons = 6

Therefore No of neutrons are 14 - 6 = 8

Since 14 is the mass no of this isotope of carbon.

That means 14 gram of this carbon will contain 6.02*10^23 ( Avogadro's number) atoms of 14C

Now one atom of 14 C contains 8 neutrons there fore 14 gram of 14C will contain 8 * (6.02*10^23)

That means

14 * 1000 mg ( I gram = 1000 mg) will have 8 * (6.02 * 10^23) neutrons.

14 mg will have [8* (6.02*10^23) ] /1000 = 8 * (6.02 * 10^20)

1 mg = [ 8 * (6.02 * 10^20) ] /14

7 mg = [8 * (6.02 * 10^20) *7 ] / 14

That will be around 24 * 10^20   because you will have to assume Avogadro's number to  be 6 * 10^23

So we have Total no of Neutrons equal to 24 * 10^20

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Now We know that mass of a neutron is 1.675 * 10^-27 kg

No of neutrons in 7 mg of 14 C = 24 * 10^20 as we calculated above.

So total mass of neutrons will be [ 1.675*10^-27 ] * [24 * 10^20]

That will be equal to 40.2 * 10^-7 kg