Question

A certain element x has four isotopes. 4.350% of x has a mass of 49.94605 amu. 83.79% of x has a mass of 51.94051 amu. 9.500% of x has a mass of 52.94065 amu. 2.360% of x has a mass of 53.93888 amu. What is the average atomic mass of element x? Express your answer numerically to four significant figures. View available hint(s)

Answer 1

Average atomic mass of an element is the sum of atomic mass of its isotopes multiplied by their respective percentage abundance.

There are four isotopes of element X:

1. 4.350 % with mass 49.94605 amu

2. 83.79% with mass 51.94051 amu

3. 9.5% with mass 52.94065 amu

4. 2.360% with mass 53.93888 amu

Thus, average atomic mass will be:

$=49.94605(\frac{4.350}{100})+51.94051(\frac{83.79}{100})+52.95065(\frac{9.5}{100})+53.93888(\frac{2.360}{100})$

Or,

$Average atomic mass=2.173 amu+43.52 amu+5.029 amu+1.273 amu=51.99 amu$

Therefore, average atomic mass of element X will be 51.99 amu (four significant figures)

Answer 2

Answer: 52.00 amu.

Explanation:

Mass of isotope 1 = 49.94605 amu

% abundance of isotope 1 = 4.350% = $\frac{4.350}{100}=0.0435$

Mass of isotope 2 =  51.94051 amu

% abundance of isotope 2 = 83.79 % = $\frac{83.79}{100}=0.8379$

Mass of isotope 3 =  52.94065 amu

% abundance of isotope 3  = 9.500 % = $\frac{9.500}{100}=0.095$

Mass of isotope 4 = 53.93888 amu

% abundance of isotope 4 = 2.360 % = $\frac{2.360}{100}=0.0236$

Formula used for average atomic mass of an element :

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

$A=\sum[(49.94605\times 0.0435)+(51.94051\times 0.8379)+(52.94065\times 0.095)+(53.93888\times 0.0236)]$

$A=52.00amu$

Therefore, the average atomic mass of an element is 52.00 amu.