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How many neutrons are there in 0.14 g of carbon-14? - Leaving Cert Chemistry - Question e - 2013

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How many neutrons are there in 0.14 g of carbon-14?

Worked Solution & Example Answer:How many neutrons are there in 0.14 g of carbon-14? - Leaving Cert Chemistry - Question e - 2013

Step 1

Step 1: Convert grams to moles

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Answer

To find the number of moles in 0.14 g of carbon-14, we use the molar mass of carbon-14, which is approximately 14 g/mol.

Calculating the moles: 0.14 ext{ g} imes rac{1 ext{ mol}}{14 ext{ g}} = 0.01 ext{ mol}

Step 2

Step 2: Calculate number of atoms

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Using Avogadro's number, which is approximately 6imes10236 imes 10^{23} atoms/mol, we can find the number of atoms in 0.01 mol:

0.01extmolimes6imes1023extatoms/mol=6imes1021extatoms0.01 ext{ mol} imes 6 imes 10^{23} ext{ atoms/mol} = 6 imes 10^{21} ext{ atoms}

Step 3

Step 3: Determine the number of neutrons

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Answer

Carbon-14 has a mass number of 14 and an atomic number of 6, which means it has 6 protons. The number of neutrons is given by the difference between the mass number and the atomic number:

14−6=8extneutrons14 - 6 = 8 ext{ neutrons}

Now, multiplying the number of atoms by the number of neutrons per atom gives:

6imes1021extatomsimes8extneutrons/atom=4.8imes1022extneutrons6 imes 10^{21} ext{ atoms} imes 8 ext{ neutrons/atom} = 4.8 imes 10^{22} ext{ neutrons}

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