The average atomic mass of naturally occurring neon is 20.18 amu.There are two c

Question

The average atomic mass of naturally occurring neon is 20.18 amu.There are two common isotopes of naturally occurring neon asindicated in the table below.

Isotope            Mass (amu)
Ne-20            19.99
Ne-22            21.99

a.) Using the info above, calculate the percent abundance of eachisotope.

b.) Calculate the number of Ne-22 atoms in a 12.55 g sample ofnaturally occurring neon.
c.) a major line in the emission spectrum of neon corresponds to afrequency of 4.34x1014s-1. Calculate thewavelength, in nanometers, of light that corresponds to this line.

Explanation / Answer

Neon has 3 naturally occurring isotopes. The masses and natural abundances of these isotopes are as follows. 1= 19.99 amu, 90.48 % 2= 20.99 amu, 0.27 % 3= 21.99 amu, 9.25 % We can let x be the fraction/percent of Ne-20 and y be the fractionof Ne-22 So, 19.99x + 21.99y = 20.18 since the average atomic mass of naturally occurring neon is 20.18amu. This can be simplified to x + y = 1 which also can be rearranged to make x = 1 - y Substituting the previous equations into each other to find onevariable, we get: 19.99(1-y) + 21.99y = 20.18 19.99 - 19.99y + 21.99y = 20.18 2y = 0.19 y = 0.095 Substitution of this value into the first equation provides thevalue for x. x = 0.905 Therefore Ne-20 = 90.48%, Ne-22 = 9.25% b) From information above, the mass fraction of Ne-22 is 0.095. This is because 9.5% of the mass is Ne-22. Similar to before, 12.55g x 0.095 = 1.192 g Ne-22 1.192 g Ne-22/21.99 g/mol = 0.0542 mol 1 mol = 6.023 x 10^23 (0.0542 mol)·(6.023 x 10^23 /mol) = 3.266 x 10^22 moleculesof Ne-22

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