Q14.

(a) The nucleus of a particular atom has a nucleon number of 14 and a proton number of 6.

(i) State what is meant by nucleon number and proton number.

The nucleon number is the sum of the number of protons and neutrons in the nucleus (OR the mass number of the nucleus).

The proton number is the number or protons in the nucleus (OR the atomic number of the nucleus).

Both have to be correctly explained for the mark. No half marks are awarded by the board.

(1 mark)

(ii) Calculate the number of neutrons in the nucleus of this atom.

14 - 6 = 8

(1 mark)

(iii) Calculate the specific charge of the nucleus, in C kg^-1.

You need to lay this out carefully - there are three marks so they want you to show clear reasoning in your working!

They give you the unit, so it is easy to work out what to do - charge on the nucleus (in coulombs) divided by the mass of the nucleus (in kilograms)

Charge on nucleus:

There are six protons - the only charged particles, and they have the same charge as an electron....

charge = 6 x 1.60 x 10^-19

charge = 9.60 x 10^-19 C

Mass of the nucleus:

There are 8 neutrons and 6 protons:

Mass = 8 (1.675 x 10^-27) + 6 (1.673 x 10^-27)

Mass = 2.34 x 10^-26 kg (the other factor is only to 3sf - so that is all that is needed)

Specific charge

= 9.60 x 10^-19/ 2.34 x 10^-26 C kg^-1

= 4.10 x 10⁷ C kg^-1

(3 marks)

(b) The specific charge of the nucleus of another isotope of the element is 4.8 × 10⁷ C kg^–1.

(i) State what is meant by an isotope.

All variations of the nuclei of atoms of the same element are isotopes. There is not such a thing as a 'normal' version of an element... although there might be a common one.

There are two things they want you to make clear:

- isotopes of an element all have nuclei containing the same number of protons as each other and

- different isotopes of the same element have different numbers of neutrons from each other

They therefore usually offer two marks for the definition of an isotope - therefore learn it!

Nuclei of isotopes of an element all contain the same number of protons as each other but different numbers of neutrons. This gives them the same chemical properties but different physical properties.

(2 marks)

(ii) Calculate the number of neutrons in this isotope.

Let

N = the nucleon number and

the mass of a nucleon be aproximated to the average of 1.674 x 10^-27

Then:

4.8 x 10⁷ = 6 x 1.60 x 10^-19/(N x 1.67 x 10^-27)

N = 6 x 1.60 x 10^-19/(1.67 x 10^-27x 4.8 x 10⁷)

 

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OR reasoned another way....

Both of these have the same number of protons, but different numbers of neutrons.

specific charge A = Q_A/m_A

specific charge B = Q_B/m_B

specific charge A /specific charge B = Q_Am_B/Q_Bm_A

But Q_A = Q_B

so, specific charge A /specific charge B = m_B/m_A

(4.10 x 10⁷)/(4.8 × 10⁷) = m_B/m_A

4.1 /4.8 = m_B/m_A

As the mass of the neutron and proton are virtually the same....

m_B/m_A = nucleon number of B/nucleon number of A

m_B/m_A = 0.854

so, nucleon number of B = 0.854 x 14 = 12

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Therefore the nucleon number of A = 12

And the number of neutrons = 12 - 6 = 6

(3 marks)

(Total 10 marks)