Probabilities are used in the quantum mechanical model of the atom because of heisenberg's uncertainty principle. this principle states that the and of an electron can be measured, but not simultaneously.

Position and momentum

Explanation:

The Heisenberg uncertainty principle also called the uncertainty principle states that the position and momentum of a particular particle cannot be measured with precision at the same time.

It means that to determine either of the two properties, we have to do that at a later time and not at the same time. Doing both at the same time will not yield a correct value for the two.

The theory was put forward by a German physicist by the name Werner Heisenberg in the year 1927.

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percent abundance for cu-63 can be shown as:

63 x + 65 (1-x) = 62.9296

65 - 62.9296 = 2 x

x = 1.035

thus, percent abundance for cu-63 is 1.035

percent abundance for cu-65 can be shown as:

63 x + 65 (1-x) = 64.9278

65 - 64.9278 = 2 x

x = 0.0361

thus, percent abundance for cu-63 is 0.0361

the mass spectrum of cu-63 showing the intense peak as, this isotope is found in nature more abundantly around 92.38 % in comparison to cu-65 which is found 62.58 % naturally