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Essential Knowledge

◼ The mass spectrum of a sample containing a single element can be used to determine the identity of the isotopes of that element and the relative abundance of each isotope in nature. (SPQ-1.B.1) Go to Section

◼ The average atomic mass of an element can be estimated from the weighted average of the isotopic masses using the mass of each isotope and its relative abundance (SPQ-1.B.2) Go to Section

◼ The mass spectrum of a sample containing a single element can be used to determine the identity of the isotopes of that element and the relative abundance of each isotope in nature. (SPQ-1.B.1)

The mass spectrum of a sample of a pure element is shown below. Calculate the average atomic mass of the element and identify the element.

*** SEE BELOW FOR WORKED OUT SOLUTION ***

From the spectrum, I can see that there are three isotopes representing the following isotopes:

Mass: 39 amu, Abundance: 93.26%

Mass: 40 amu, Abundance: 0.01%

Mass: 41 amu, Abundance: 6.73%

I will find the weighted average of the isotopic masses using the formula below.

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑨𝒕𝒐𝒎𝒊𝒄 𝑴𝒂𝒔𝒔 = ∑ 𝒏 (𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝒂𝒃𝒖𝒏𝒅𝒂𝒏𝒄𝒆 𝒐𝒇 𝒊𝒔𝒐𝒕𝒐𝒑𝒆 𝒏) × (𝒎𝒂𝒔𝒔 𝒐𝒇 𝒊𝒔𝒐𝒕𝒐𝒑𝒆 𝒏)

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑨𝒕𝒐𝒎𝒊𝒄 𝑴𝒂𝒔𝒔 = (𝟎. 𝟗𝟑𝟐𝟔 × 𝟑𝟗 𝒂𝒎𝒖) + (𝟎. 𝟎𝟎𝟎𝟏 × 𝟒𝟎 𝒂𝒎𝒖) + (𝟎. 𝟎𝟔𝟕𝟑 × 𝟒𝟏 𝒂𝒎𝒖)

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑨𝒕𝒐𝒎𝒊𝒄 𝑴𝒂𝒔𝒔 = 𝟑𝟔. 𝟑𝟕𝟏𝟒 𝒂𝒎𝒖 + 𝟎. 𝟎𝟎𝟒𝟎 𝒂𝒎𝒖 + 𝟐. 𝟕𝟓𝟗𝟑 𝒂𝒎𝒖

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑨𝒕𝒐𝒎𝒊𝒄 𝑴𝒂𝒔𝒔 = 𝟑𝟗. 𝟏𝟑𝟒𝟕 𝒂𝒎𝒖

The average atomic mass of the element is 39.1347 amu.

Answer: The identity of the element is potassium, K. The calculated average atomic mass of 39.1347 amu is closest to the average atomic mass given on the periodic table for potassium.

◼ The average atomic mass of an element can be estimated from the weighted average of the isotopic masses using the mass of each isotope and its relative abundance (SPQ-1.B.2)

Use the mass spectrum below to fill out the information in the table about each isotope.

  
    Isotope
    Proton
    Neutron
    Mass (amu)
    Relative Abundance (%)

*** SEE BELOW FOR WORKED OUT SOLUTION ***

  
    Isotope
    Proton
    Neutron
    Mass (amu)
    Relative Abundance (%)
  
    Strontium-88
    38
    50
    88
    82.58%
  
    Strontium-87
    38
    49
    87
    7.00%
  
    Strontium-86
    38
    48
    86
    9.86%
  
    Strontium-84
    38
    46
    84
    0.56%

Try it yourself …

Based on the information show on the right,

(a) what is the most likely identity of this element?

(b) Fill in the table below.

  
    Mass Number
    Protons
    Neutrons
  
    79
    
    81

(c) Which isotope of this element, mass number = 79 or mass number = 81, is more abundant in nature? Justify your answer.

Check your answer here: [PART A] [PART B] [PART C]

1.2 Mass Spectra of Elements

Essential Knowledge