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Question: The three stable isotopes of neon \[{^{20}_{10}}Ne\] , \[{^{21}_{10}}Ne\] and \[{^{22}_{10}}Ne\] hav...

The three stable isotopes of neon 1020Ne{^{20}_{10}}Ne , 1021Ne{^{21}_{10}}Ne and 1022Ne{^{22}_{10}}Ne have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of three isotopes are 19.99u, 20.99u and 21.99u, respectively. Obtain the average atomic mass of neon.

Explanation

Solution

Hint: Try to recall that the average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance. Now, by using this you can easily calculate the average atomic mass of neon.

Complete step by step solution:
It is known to you that the average mass of an atom of a given element, based on the occurrence and mass of the various isotopes as they are found in the crust and atmosphere.
An element does not have an absolute atomic mass. The atomic mass is average because it is calculated on the basis of % of the isotopes present in nature.
Calculation:
Atomic mass of isotope 1020Ne{^{20}_{10}}Ne =20
Atomic mass of isotope 1021Ne{^{21}_{10}}Ne =21
Atomic mass of isotope 1022Ne{^{22}_{10}}Ne =22
% of isotope 1020Ne{^{20}_{10}}Ne =90.51
% of isotope 1021Ne{^{21}_{10}}Ne =0.27
% of isotope 1022Ne{^{22}_{10}}Ne =9.22
Average atomic mass of neon, A=

=(% of 2010Ne×atomic mass of 2010Ne)+(% of 2110Ne×atomic mass of 2110Ne)+(% of 2210Ne×atomic mass of 2210Ne)100 =(90.51×20)+(0.27×21)+(9.22×22)100 =1810.2+5.67+202.84100 =2018.71100=20.18u  = \dfrac{{\left( {\% {\text{ }}of{{\text{ }}^{20}}_{10}Ne \times atomic{\text{ mass of}}{{\text{ }}^{20}}_{10}Ne} \right) + \left( {\% {\text{ }}of{{\text{ }}^{21}}_{10}Ne \times atomic{\text{ mass of}}{{\text{ }}^{21}}_{10}Ne} \right) + \left( {\% {\text{ }}of{{\text{ }}^{22}}_{10}Ne \times atomic{\text{ mass of}}{{\text{ }}^{22}}_{10}Ne} \right)}}{{100}} \\\ = \dfrac{{\left( {90.51 \times 20} \right) + \left( {0.27 \times 21} \right) + \left( {9.22 \times 22} \right)}}{{100}} \\\ = \dfrac{{1810.2 + 5.67 + 202.84}}{{100}} \\\ = \dfrac{{2018.71}}{{100}} = 20.18u \\\

Note: It should be remembered to you that neon is used for making high-voltage indicators and switching gear, lasers, etc. Also, liquid neon is used as the cryogenic refrigerant.
Also, you should be remembered that neon is used in beacon light as a safety signal for air navigators because its light has fog penetration power.