Naturally occurring element X exists in three isotopic forms: X-28 (27.977 amu, 92.23% abundance), X-29 (28.976 amu, 4.67% abundance), and X-30 (29.974 amu, 3.10% abundance). What is the identity of element X?

[tex]Average\ atomic\ mass=(\frac {\%\ of\ the\ first\ isotope}{100}\times {Mass\ of\ the\ first\ isotope})+(\frac {\%\ of\ the\ second\ isotope}{100}\times {Mass\ of\ the\ second\ isotope})+(\frac {\%\ of\ the\ third\ isotope}{100}\times {Mass\ of\ the\ third\ isotope})[/tex]

Given that:

For first isotope, X-28 :

% = 92.23 %

Mass = 27.977 amu

For second isotope, X-29:

% = 4.67 %

Mass = 28.976 amu

For third isotope, X-30:

% = 3.10 %

Mass = 29.974 amu

Thus,

[tex]Average\ atomic\ mass=\frac{92.23}{100}\times {27.977}+\frac{4.67}{100}\times {28.976}+\frac{3.10}{100}\times {29.974}[/tex]

[tex]Average\ atomic\ mass=25.8031871+1.3531792+0.929194\ amu[/tex]

Average atomic mass = 28.0855603 amu ≅ 28.086 amu

This mass corresponds to Silicon, ( Z = 14).