The average atomic mass of lithium is 6.941 amu. Lithium has two naturally occurring isotopes, 6Li (7.52%) and 7Li (92.48%). The mass of 6Li is 6.0151 amu. What is the isotopic mass of 7Li ?
The Correct Answer and Explanation is :
To find the isotopic mass of ( ^7Li ), we can use the concept of the weighted average, which is based on the contribution of each isotope to the overall atomic mass of lithium.
The formula for calculating the average atomic mass is:
[
\text{Average Atomic Mass} = ( \text{mass of isotope 1} \times \text{fraction of isotope 1} ) + ( \text{mass of isotope 2} \times \text{fraction of isotope 2} )
]
In this case, we know the following:
- The average atomic mass of lithium is 6.941 amu.
- ( ^6Li ) has a mass of 6.0151 amu and makes up 7.52% (or 0.0752 in fractional form) of naturally occurring lithium.
- ( ^7Li ) has an unknown mass, which we will denote as ( m_7 ), and makes up 92.48% (or 0.9248 in fractional form) of naturally occurring lithium.
Substituting these values into the equation:
[
6.941 = (6.0151 \times 0.0752) + (m_7 \times 0.9248)
]
First, calculate the contribution of ( ^6Li ):
[
6.0151 \times 0.0752 = 0.4527
]
Now, plug this into the equation:
[
6.941 = 0.4527 + (m_7 \times 0.9248)
]
Next, isolate ( m_7 ):
[
6.941 – 0.4527 = m_7 \times 0.9248
]
[
6.4883 = m_7 \times 0.9248
]
[
m_7 = \frac{6.4883}{0.9248}
]
[
m_7 = 7.02 \, \text{amu}
]
Thus, the isotopic mass of ( ^7Li ) is approximately 7.02 amu.
Explanation:
The average atomic mass of an element is a weighted mean of the masses of its isotopes. Since isotopes of an element have the same chemical behavior but different masses, their relative abundances directly affect the average atomic mass. By knowing the mass of ( ^6Li ) and its abundance, we can use the formula above to find the mass of ( ^7Li ). The large difference in natural abundances of these isotopes explains why the atomic mass of lithium is closer to the mass of ( ^7Li ) than to ( ^6Li ). This method ensures that the average atomic mass takes into account the relative contributions of each isotope.