Question

there are two stable isotopes of gallium, $^{69}$ga and $^{71}$ga. calculate the average atomic mass from the following data from the mass spectrometer.
isotope % abundance relative mass mass contribution
ga-69 60.1089 68.925580 amu
ga-71 39.8929 70.924701 amu
calculate the average atomic mass for gallium
isotope % abundance relative mass mass contribution
ga-69 60.1089 68.925580 amu 4143.0408 amu
ga-71 39.8929 70.924701 amu 2829.3920 amu
6972.4328 amu
isotope abundance relative mass mass contribution
ga-69 0.601089 68.925580 amu 41.430408 amu

Explanation:

Step1: Convert percentage abundances to decimals

For Ga - 69, the abundance as a decimal is $a_{69}=60.1089\div100 = 0.601089$. For Ga - 71, the abundance as a decimal is $a_{71}=39.8929\div100=0.398929$.

Step2: Calculate mass - contributions

The mass - contribution of Ga - 69 is $m_{69}=a_{69}\times m_{r69}=0.601089\times68.925580\approx41.430408$ amu. The mass - contribution of Ga - 71 is $m_{71}=a_{71}\times m_{r71}=0.398929\times70.924701\approx28.293920$ amu.

Step3: Calculate the average atomic mass

The average atomic mass $M = m_{69}+m_{71}=41.430408 + 28.293920=69.724328$ amu.

Answer:

69.724328 amu