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Average Atomic Mass for JEE

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Last updated date: 16th Jul 2024
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What is Atomic Mass and Mass Number?

One of the basic physical properties of matter is mass. We usually refer to the term atomic mass for mass of an atom. This mass is expressed in atomic mass units or amu. The atomic mass of elements is due to the subatomic particles present in the atomic nucleus, and these include the electrons, protons and neutrons. Electrons are generally ignored because their mass is much smaller than the other two particles.


The sum of the total number of protons and neutrons present in an atomic nucleus are referred to as the mass number of that atom. Weight of each proton and neutron is one atomic mass unit, therefore multiplying the mass number by one gives the atomic mass of that atom. For one element, all the atoms have the same number of protons in their nucleus, also known as the atomic number of that element. However, the number of neutrons can vary in atoms of one element. Such atoms are called isotopes. In this topic we’ll learn about isotopes, we’ll also learn what is average atomic mass.


Isotopes and Average Atomic Mass

To define average atomic mass, one must be aware of the concept of isotopes. The number of neutrons present in the nucleus of atoms of the same element can be different and therefore, atoms with the same atomic number have different values of mass numbers and atomic masses. Such atoms are known as isotopes.: For example, carbon-12, carbon-13, and carbon-14 are three isotopes of carbon. Carbon-12 contains a total of 6 neutrons and has mass of 12 amu, carbon-13 contains a total of 7 neutrons and has mass of 13 amu, and carbon-14 contains a total of 8 neutrons and has mass of 14 amu.


There are many elements that exist naturally as more than one isotope, however the relative abundance of those isotopes is not the same. Taking this into consideration the concept of average atomic mass was discovered.


The average atomic mass of an element is given by the sum of the masses of isotope, each multiplied by its relative abundance percentage. The average atomic mass formula can be given by-

  • $\dfrac{\sum \% \text{Abundance} \times \text{Atomic Mass}}{100}$


Average Atomic Mass Examples

Now that we have learned how to find average atomic mass. Let’s calculate it for some common elements.


Carbon: Carbon Has Three Isotopes

  • C-12 with relative abundance of 98.89 % and atomic mass of 12 amu.

  • C-13 with relative abundance of 1.108 % and atomic mass of 13.00335 amu.

  • C-14 with relative abundance of 210-10 % and an atomic mass of 14.00317 amu.

  • Percentage are converted into fractions by dividing them with 100.

The average atomic mass of carbon is = 

(0.98892) (12) + (0.01108) (13.00335) + (210-10) (14.00317) = 12.011 amu


Chlorine: Chlorine Has Two Major Isotopes.

  • Chlorine-35 (Cl-35) with relative abundance of 75.77 % and atomic mass of 35 amu.

  • Chlorine-37 (Cl-37) with relative abundance of 0.037 % and atomic mass of 37 amu.

  • Percentage are converted into fractions by dividing them with 100.

The average atomic mass of chlorine is = 

(0.7577) (35) + (0.2423) (37) = 35.48 amu.


Copper: Copper Has Two Major Isotopes.

  • Copper-63 with relative abundance of 69.17 % and atomic mass of 62.930 amu

  • Copper-65 with relative abundance of 30.83 % and atomic mass of 64.928 amu

  • Percentage are converted into fractions by dividing them with 100.

The average atomic mass of copper is = 

(0.6917) (62.930) + (0.3083) (64.928) = 63.546 amu.


Conclusion

For many elements we don’t get isotopically pure chemicals as they exist as an isotopic mixture in nature and therefore, for accurate weighing we can’t use atomic mass. The average atomic mass is useful because its value is equal to molar mass, this helps in weighing and reacting a solid with other reagents. Average atomic mass can be calculated by knowing the atomic masses and natural abundances of the isotopes of a given element. If the value of average atomic mass is known, the individual isotopic abundance percentage can also be calculated.

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FAQs on Average Atomic Mass for JEE

1. Is atomic mass and average atomic mass same?

The two terms atomic mass and average atomic mass might sound identical to each other but they are different. The key difference between atomic mass and average atomic mass is that atomic mass is the mass of the subatomic particles in an atom calculated by adding the number of protons and neutrons in the nucleus of the given atom. Average atomic mass on the other hand is calculated by taking the isotopes of an element into the consideration. It depends on both the atomic mass as well as natural abundance of the isotope.

2. What is the average atomic mass of hydrogen?

Hydrogen has three isotopes- Hydrogen with atomic mass 1.0078, deuterium with atomic mass 2.0141 and tritium with atomic mass 3.016 However, only hydrogen and deuterium are stable isotopes with natural abundances 99.985 and 0.015 respectively. Tritium being radioactive has negligible natural abundance. 


The average atomic mass of hydrogen is $=\dfrac{(99.985 \times 1.0078)+(0.015 \times 2.0141)}{100}=1.0079~amu$

3. Given the average atomic weight of copper = 63.546, what is the percentage abundance of its isotopes?

Copper has two stable isotopes Cu-63 with mass 62.9296 and Cu-65 with mass 64.9278

  • Let’s assume natural abundance of  Cu-63 = x and of Cu-65 = 1 - x

(Because, these two are the stable naturally occurring isotopes, therefore x + (1 - x) = 100 % or if taking in fractions we can divide it by 100 and say, x + (1 - x) = 1)

  • We know Average atomic mass = Sum of product of atomic masses and natural abundance of isotopes

For copper Average atomic mass (63.546) = (62.9296) (x) + (64.9278) (1 - x) 

  • 62.9296x + 64.9278-64.9278x = 63.546

  • By solving this we get,

x = 0.6915 or 69.15 %, 1 - x = 1-0.6915 = 0.3083 or 30.83%