We can use the GetConstant command to get the definition of the physical constant , an elementary charge.

This provides us with a relationship that defines an elementary charge in terms of the Planck Constant (h), the fine structure constant (), permeability of a vacuum () and the speed of light (c).  Each of these constants is also defined in the ScientificConstants package.

The value of  can be manually calculated from the individual constants, or we can obtain its value directly using the evalf command.

We can obtain more information on this constant, such as its units.

For a list of physical constants in the ScientificConstants package, see Initial Physical Constants.

We can use the GetElement command to access a full description of the properties of elements of the Periodic Table of Elements.

For example, let's review the properties of Platinum (Pt).

We can also extract the standard atomic weight of platinum.

In the following example, we determine how many molecules of caffeine are in a 250 gram sample.

The chemical formula for caffeine is .  Thus, the molecular weight is:

which, in the current default system of units, SI, is measured in kilograms (kg). However, molecular weight is typically expressed in atomic mass units (amu). To convert a measurement between units, use the convert/units function.

By definition, the number of atomic mass units per molecule is equal to the number of grams per mole. Hence, divide 250 by the above result.

which is the number of moles in the sample.

To calculate the number of molecules, multiply the above result by Avogadro's constant.

In the following example, we plot the decrease in the radioactive decay activity for a sample of radium-229.

The expression for the activity is:

where is the initial activity, is the mean lifetime of the isotope, and is the elapsed time.

The mean lifetime is related to the half-life by

Plot with

In the following example, we determine the radius of a geostationary orbit.

The expression for circular orbital velocity around a spherically symmetric body is:

where G is the gravitational constant, M is the mass of the body, and R is the radius of orbit.

Now, for geostationary orbit, an orbital velocity of 2 π R meters per day is required, which in meters per second is:

Equate this to .

Solve for R. To disregard the non-real solutions, use the RealDomain package.

The use statement creates a RealDomain environment in which computations are performed under the assumption that the underlying number system is the real numbers.

Replace G with its value and M with the mass of the Earth, then evaluate.

The result is the radius in kilometers (km) of a geostationary orbit.