Question

The element silver consists of two isotopes 107Ag (atomic mass = 106.905) and 109Ag (atomic mass = 108.904). The average atomic mass of silver is 107.87. The natural abundances of 107Ag and 109Ag are _____% and _____%, respectively.

Answer 1

52% and 48%

Step-by-step explanation:

Ok. Isotopes of an element exists with slightly different properties, these atoms have the same number of electrons and protons but different number of neutrons, hence the difference in mass number..

so you have Silver(107) and Silver(109) existing but its overall mass number is 107.87. This is calculated by the natural presence in which these elements exist.

So you are given the average and asked to calculate the percentages so we work in the reverse

1. layout what you have in a table

atom mass number variable

Ag 107 106.905 x

Ag 109 108.904 1-x

2. write out an equation

107.87 = (106.905)(x) + (108.904)(1-x)

3. expand your brackets using the distributive law

107.87 = 106.905x + 108.904 - 108.904x

4. put like terms together

107.87 - 108.904 = 106.905x - 108.904x

5. subtract

you should get -1.034 = -1.999

6. divide both sides by -1.999

`( - 1.034)/( - 1.999) = ( - 1.999x)/( - 1.999)`

so u get 0.517.... = x

So u convert that to a percentage to the nearest whole and you get 52%

Now remember the other value was equivalent to 1-x so u subtract the 0.517 from 1 to get the other value

and it is 0.483... rounded up to 48%

and voila

Answer 2

52% and 48%

Step-by-step explanation:

Ok. Isotopes of an element exists with slightly different properties, these atoms have the same number of electrons and protons but different number of neutrons, hence the difference in mass number..

so you have Silver(107) and Silver(109) existing but its overall mass number is 107.87. This is calculated by the natural presence in which these elements exist.

So you are given the average and asked to calculate the percentages so we work in the reverse

1. layout what you have in a table

atom mass number variable

Ag 107 106.905 x

Ag 109 108.904 1-x

2. write out an equation

107.87 = (106.905)(x) + (108.904)(1-x)

3. expand your brackets using the distributive law

107.87 = 106.905x + 108.904 - 108.904x

4. put like terms together

107.87 - 108.904 = 106.905x - 108.904x

5. subtract

you should get -1.034 = -1.999

6. divide both sides by -1.999

`( - 1.034)/( - 1.999) = ( - 1.999x)/( - 1.999)`

so u get 0.517.... = x

So u convert that to a percentage to the nearest whole and you get 52%

Now remember the other value was equivalent to 1-x so u subtract the 0.517 from 1 to get the other value

and it is 0.483... rounded up to 48%

and voila