Question

argon (ar) has three naturally occurring isotopes. $^{36}$ar has an atomic mass of 35.968 amu and a percent abundance of 0.334%. $^{38}$ar has an atomic mass of 37.963amu and a percent abundance of 0.0630%. $^{40}$ar has an atomic mass of 39.962 amu and a percent abundance of 99.603%. calculate the average atomic mass of argon. how does this compare to the value on the periodic table.

the average atomic mass of gallium is 69.723 amu. gallium has two naturally occurring isotopes, $^{69}$ga and $^{71}$ga. $^{69}$ga has a mass of 68.926 amu and a natural abundance of 60.108%. calculate the mass and natural abundance of $^{71}$ga.

a fictional element \oh\ consists of two isotopes. $^{252}$oh has a mass of 251.908 amu and a percent abundance of 78.095%. $^{255}$oh has a mass of 255.077 amu. calculate the average atomic mass.

Explanation:

First Problem: Average Atomic Mass of Argon

Step1: Convert % to decimals

$0.334\% = 0.00334$, $0.0630\% = 0.000630$, $99.603\% = 0.99603$

Step2: Calculate isotope contributions

$35.968 \times 0.00334 = 0.1201$, $37.963 \times 0.000630 = 0.02392$, $39.962 \times 0.99603 = 39.804$

Step3: Sum contributions for average

$0.1201 + 0.02392 + 39.804 = 39.948$

Step1: Find abundance of $^{71}$Ga

$100\% - 60.108\% = 39.892\% = 0.39892$

Step2: Set up average mass equation

Let $m$ = mass of $^{71}$Ga.
$69.723 = (68.926 \times 0.60108) + (m \times 0.39892)$

Step3: Solve for $m$

$69.723 = 41.430 + 0.39892m$
$0.39892m = 69.723 - 41.430 = 28.293$
$m = \frac{28.293}{0.39892} = 70.924$

Step1: Convert % to decimals

$78.095\% = 0.78095$, $100\% - 78.095\% = 21.905\% = 0.21905$

Step2: Calculate isotope contributions

$251.908 \times 0.78095 = 196.73$, $255.077 \times 0.21905 = 55.875$

Step3: Sum contributions for average

$196.73 + 55.875 = 252.605$

Answer:

The average atomic mass of argon is 39.948 amu. This matches the periodic table value of ~39.95 amu (the slight difference is due to rounding during calculations).

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Second Problem: Mass and Abundance of $^{71}$Ga