Question

Gallium has two naturally occurring isotopes: 69ga with a mass of 68.9256 amu and a natural abundance of 60.11% and 71ga. use the atomic mass of gallium from the periodic table to find the mass of gallium-71. express the mass in atomic mass units to two de

Answer 1

Answer: The atomic mass of gallium-71 is 70.92 amu.

Step-by-step explanation:

Mass of isotope Ga-69 = 68.9256 amu

% abundance of isotope Ga-69 = 60.11% =
`(60.11)/(100)=0.6011`

Mass of isotope Ga-71 = ?

% abundance of isotope Ga-71 = (100-60.11)% =
`(39.89)/(100)=0.3989`

Formula used for average atomic mass of an element :

`\text{ Average atomic mass of an element}=\sum(\text{atomic mass of an isotopes}* {{\text { fractional abundance}})`

`\text{ Average atomic mass of an element}=69.723amu`

`69.723 =\sum[(68.9256* 0.6011)+(x* 0.3989)]`

`x=70.92amu`

Therefore, the atomic mass of gallium-71 is 70.92 amu.

Answer 2

There are two naturally occurring isotopes of gallium: mass of Ga-69 isotope is 68.9256 amu and its percentage abundance is 60.11%, let the mass of other isotope that is Ga-71 be X, the percentage abundance can be calculated as:

%Ga-71=100-60.11=39.89%

Atomic mass of an element is calculated by taking sum of atomic masses of its isotopes multiplied by their percentage abundance.

Thus, in this case:

Atomic mass= m(Ga-69)×%(Ga-69)+X×%(Ga-71)

From the periodic table, atomic mass of Ga is 69.723 amu.

Putting the values,

`69.723 amu=(68.9256 amu)((60.11)/(100))+X((39.89)/(100))`

Thus,

`69.723 amu=41.4312 amu+X((39.89)/(100))`

Rearranging,

`X=(69.723 amu-41.4312 amu)/(0.3989)=70.9246 amu`

Therefore, mass of Ga-71 isotope is 70.9246 amu.