How would you determine the number of proton-proton pairs, the number of neutron-neutron pairs, and the...

How would you determine the number of proton-proton pairs, the number of neutron-neutron pairs, and the number of neutron-neutron pairs in an atom given its atomic number and mass number? Hence show that Carbon has 15 proton-proton pairs and 10 neutron-neutron pairs.

Solutions

Expert Solution

The number of proton-proton and neutron-neutron pair is determined by the nuclear configuration of nucleons (shell model).

As you can see that for Z=8, we have 4 pairs of protons 1 pair in 1S_1/2, 2 pairs in 1P_1/2 and 1 pair in 1P_1/2. Similarly neutrons also have 4 pairs.

NOW AS FAR AS CARBON IS CONCERNED, A typical CARBON ATOM ( 12C₆) HAS 6 number of protons and and 6 numbers of neutrons inside collectively known as nucleons. So if we fill up the number of protons and neutron according to the shell model we will have -

Z=6, (1S_1/2 )²(1P_3/2)⁴ ---> 3 pairs of protons.

N= , (1S_1/2 )²(1P_3/2)⁴ ---> 3 pairs of neutrons.

So a typical carbon atom cannot have 15 proton proton pairs and 10 neutron neutron pairs as it has way too less number of nucleons to form such number of pairs.

However, carbon has 15 different types of known isotopes ranging from 8C₆ to 22C₆.

The 22C₆ isotope has Z=6 (3 pairs of protons) and N=A-Z=22-6=16 (8 pairs of neutrons).

genius_generous answered 1 year ago

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