Question

The three silicon isotopes have atomic masses and relative abundances of 27.9769 amu (92.2297%), 28.9765 amu (4.6832%) and 29.9738 amu (3.0872%). What is the atomic mass of silicon?

Answer 1

To calculate the atomic mass of silicon (Si), we need to consider the atomic masses and relative abundances of its isotopes.

Given: Isotope 1: Atomic mass = 27.9769 amu, Relative abundance = 92.2297% Isotope 2: Atomic mass = 28.9765 amu, Relative abundance = 4.6832% Isotope 3: Atomic mass = 29.9738 amu, Relative abundance = 3.0872%

Step 1: Convert the relative abundances to decimal form. Relative abundance of isotope 1 = 92.2297% = 0.922297 Relative abundance of isotope 2 = 4.6832% = 0.046832 Relative abundance of isotope 3 = 3.0872% = 0.030872

Step 2: Calculate the weighted average atomic mass. Atomic mass of Si = (Atomic mass of isotope 1 × Relative abundance of isotope 1) + (Atomic mass of isotope 2 × Relative abundance of isotope 2) + (Atomic mass of isotope 3 × Relative abundance of isotope 3)

Atomic mass of Si = (27.9769 amu × 0.922297) + (28.9765 amu × 0.046832) + (29.9738 amu × 0.030872)

Atomic mass of Si ≈ 25.77065 amu + 1.35485348 amu + 0.924858376 amu

Atomic mass of Si ≈ 28.050361856 amu

Therefore, the atomic mass of silicon (Si) is approximately 28.0504 amu.