The Atomic Masses Of ${}_3^6\text{Li}$ And ${}_3^7\text{Li}$ Are 6.0151 Amu And 7.0160 Amu, Respectively. Calculate The Natural Abundances Of These Two Isotopes. The Average Atomic Mass Of Li Is 6.941 Amu.

Mar 1, 2025 by ADMIN 206 views

**The Atomic Masses of Lithium Isotopes: Calculating Natural Abundances**

Introduction

Lithium (Li) is a chemical element with the atomic number 3. It is a soft, silvery-white alkali metal that is highly reactive. Lithium has two naturally occurring isotopes: ${}_3^6\text{Li}$ and ${}_3^7\text{Li}$ . The atomic masses of these isotopes are 6.0151 amu and 7.0160 amu, respectively. In this article, we will calculate the natural abundances of these two isotopes using the average atomic mass of lithium.

The Average Atomic Mass of Lithium

The average atomic mass of lithium is 6.941 amu. This value is a weighted average of the atomic masses of the two naturally occurring isotopes. To calculate the natural abundances of these isotopes, we need to use the following equation:

\text{Average Atomic Mass} = (\text{Abundance of Isotope 1} \times \text{Atomic Mass of Isotope 1}) + (\text{Abundance of Isotope 2} \times \text{Atomic Mass of Isotope 2})

Calculating the Natural Abundances of Lithium Isotopes

Let's assume that the abundance of ${}_3^6\text{Li}$ is x and the abundance of ${}_3^7\text{Li}$ is (1 - x). We can now plug in the values into the equation:

6.941 = (x \times 6.0151) + ((1 - x) \times 7.0160)

To solve for x, we can expand the equation:

6.941 = 6.0151x + 7.0160 - 7.0160x

Combine like terms:

6.941 = 7.0160 - 0.9999x

Subtract 7.0160 from both sides:

-0.0759 = -0.9999x

Divide both sides by -0.9999:

x = \frac{-0.0759}{-0.9999}

x = 0.0758

This means that the abundance of ${}_3^6\text{Li}$ is approximately 7.58%.

Calculating the Abundance of ${}_3^7\text{Li}$

Since the abundance of ${}_3^6\text{Li}$ is 7.58%, the abundance of ${}_3^7\text{Li}$ is (1 - 0.0758) = 0.9242 or 92.42%.

Conclusion

In this article, we calculated the natural abundances of the two naturally occurring isotopes of lithium: ${}_3^6\text{Li}$ and ${}_3^7\text{Li}$ . Using the average atomic mass of lithium, we found that the abundance of ${}_3^6\text{Li}$ is approximately 7.58% and the abundance of ${}_3^7\text{Li}$ is approximately 92.42%. These values are essential in understanding the properties and behavior of lithium in various chemical and physical processes.

References

Atomic Masses of the Elements 2003. Journal of Physical and Chemical Reference Data, 32(2), 201-346.
Lithium. In Encyclopedia Britannica.
Isotopes of Lithium. In Wikipedia.

Q: What are the two naturally occurring isotopes of lithium?

A: The two naturally occurring isotopes of lithium are ${}_3^6\text{Li}$ and ${}_3^7\text{Li}$ .

Q: What are the atomic masses of these isotopes?

A: The atomic masses of ${}_3^6\text{Li}$ and ${}_3^7\text{Li}$ are 6.0151 amu and 7.0160 amu, respectively.

Q: How are the natural abundances of these isotopes calculated?

A: The natural abundances of these isotopes are calculated using the average atomic mass of lithium. The equation for this calculation is:

\text{Average Atomic Mass} = (\text{Abundance of Isotope 1} \times \text{Atomic Mass of Isotope 1}) + (\text{Abundance of Isotope 2} \times \text{Atomic Mass of Isotope 2})

Q: What is the average atomic mass of lithium?

A: The average atomic mass of lithium is 6.941 amu.

Q: What is the abundance of ${}_3^6\text{Li}$ ?

A: The abundance of ${}_3^6\text{Li}$ is approximately 7.58%.

Q: What is the abundance of ${}_3^7\text{Li}$ ?

A: The abundance of ${}_3^7\text{Li}$ is approximately 92.42%.

Q: Why are the natural abundances of lithium isotopes important?

A: The natural abundances of lithium isotopes are essential in understanding the properties and behavior of lithium in various chemical and physical processes.

Q: Can the natural abundances of lithium isotopes be changed?

A: Yes, the natural abundances of lithium isotopes can be changed through various processes such as nuclear reactions or chemical reactions.

Q: How do the natural abundances of lithium isotopes affect the properties of lithium?

A: The natural abundances of lithium isotopes affect the properties of lithium such as its density, melting point, and boiling point.

Q: Can the natural abundances of lithium isotopes be used to determine the age of a sample?

A: Yes, the natural abundances of lithium isotopes can be used to determine the age of a sample through radiometric dating.

Q: What are some of the applications of lithium isotopes?

A: Some of the applications of lithium isotopes include:

Nuclear reactors
Medical applications
Space exploration
Geological dating

Q: Can lithium isotopes be used as a fuel source?

A: Yes, lithium isotopes can be used as a fuel source in nuclear reactors.

Q: What are some of the challenges associated with working with lithium isotopes?

A: Some of the challenges associated with working with lithium isotopes include:

Handling and storage
Safety concerns
Cost

Q: Can lithium isotopes be used in the production of batteries?

A: Yes, lithium isotopes can be used in the production of batteries.

Q: What are some of the benefits of using lithium isotopes in batteries?

A: Some of the benefits of using lithium isotopes in batteries include:

High energy density
Long cycle life
Low self-discharge rate

Q: Can lithium isotopes be used in the production of other materials?

A: Yes, lithium isotopes can be used in the production of other materials such as ceramics, glass, and semiconductors.

Q: What are some of the benefits of using lithium isotopes in the production of other materials?

A: Some of the benefits of using lithium isotopes in the production of other materials include:

Improved properties
Increased durability
Enhanced performance