Question

The atomic weight of Ne is 20.2. Ne is a mixture of \[N{e^{20}}\] and \[N{e^{22}}\]. The relative abundance of the heavier isotope is:
A. \[90\% \]
B. \[20\% \]
C. \[40\% \]
D. \[10\% \]

Answer 1

Hint: Isotopes can be basically explained as atoms having the same atomic number, but different atomic mass number. This means that the number of protons and electrons in the given atoms are the same, but they differ in the number of neutrons present in them.

Complete Step-by-Step answer:
Now, many elements in the periodic table exist in various forms of their isotopes. Now since the different isotopes have different values for their atomic mass numbers, it is difficult to assign the atomic mass number of any one particular isotope, for the entire element.
The solution that was found to this problem is that we take the sum of abundances of each isotope and multiply it with their corresponding atomic mass numbers. This gives us a generalised average value that can be justified for the existence of all the isotopes of the element.
The element under consideration is Neon. Neon has two isotopes namely, \[N{e^{20}}\] and \[N{e^{22}}\]. The average atomic mass can be calculated as:
Average atomic mass number = \[(\% {\text{ }}abundance{\text{ }}of)(atomic{\text{ }}mass{\text{ }}of){\text{ }}\]\[ + \]
                                                          \[(\% {\text{ }}abundance{\text{ }}of)({\text{ }}atomic{\text{ }}mass{\text{ }}of)\]
20.2 \[ = \left( x \right)\left( {20} \right) + \left( {100 - x} \right)\left( {22} \right)\]
20.2 \[ = 20x + 2200 - 22x{\text{ }} = 2200-2x\]
2x \[ = 2200-20.2 = 2179.8\]
x = 1089.9
Hence, \[x\% = 1089.9/100 = 10.89\% \]
This value can be rounded off to \[10\% \]
Hence, we get that the relative abundance of the heavier isotope, i.e. \[N{e^{22}}\] is \[10\% \]

Hence, Option D is the correct option.

Note: Scientists estimate that the elements that occur naturally on Earth (some only as radioisotopes) occur as 339 isotopes (nuclides) in total. Only 252 of these naturally occurring nuclides are stable in the sense of never having been observed to decay as of the present time.