Using Scientific Constants in Maple
Go to Maple Portal Maple Portal for Engineers

Introduction


Maple includes an extensive ScientificConstants package that provides access to the values of various constant physical quantities.
Such values can be used to solve equations in fields such as chemistry and physics. The ScientificConstants package also provides the units for each of the constant values, allowing for greater understanding of the equation as well as units matching for error checking of the solution.
The quantities available in the ScientificConstants package are divided into two distinct categories:
2.

properties of the chemical elements (and their isotopes)

This document will highlight the uses of the ScientificConstants package and provide some examples of its use.


Accessing the Package


There are two ways of accessing the ScientificConstants Package.
We can use the full name of the command, calling the package name, and then the specific command in square brackets.
 (1) 
Alternatively, we can also load the package by using the with command. This enables the use of the short form of the command name. Use of the with command is especially convenient if you will be calling multiple functions from a specific package within a document.
 (2) 
 (3) 


Highlights of the Package


The following are examples of some of the commands available in the ScientificConstants package. For a full listing of commands and their descriptions, see the ScientificConstants help page.

GetConstant


We can use the GetConstant command to get the definition of the physical constant , an elementary charge.
 (4) 
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.
 (5) 
The value of can be manually calculated from the individual constants, or we can obtain its value directly using the evalf command.
 (6) 
We can obtain more information on this constant, such as its units.
 (7) 
For a list of physical constants in the ScientificConstants package, see Initial Physical Constants.


GetElement


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).
 (8) 
We can also extract the standard atomic weight of platinum.
 (9) 

GetIsotopes


Finally, using the GetIsotopes command, we can access all instances of platinum.
 (10) 




Examples


The following examples highlight the use of the ScientificConstants package in the fields of Science and Engineering.

Molecular Weight


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:
 (11) 
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.
 (12) 
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.
 (13) 
which is the number of moles in the sample.
To calculate the number of molecules, multiply the above result by Avogadro's constant.
 (14) 


Radioactive Decay


In the following example, we plot the decrease in the radioactive decay activity for a sample of radium229.
The expression for the activity is:
 (15) 
where is the initial activity, is the mean lifetime of the isotope, and is the elapsed time.
The mean lifetime is related to the halflife by
 (16) 
Plot with


Radius of a Geostationary Orbit


In the following example, we determine the radius of a geostationary orbit.
The expression for circular orbital velocity around a spherically symmetric body is:
 (17) 
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:
 (18) 
Equate this to .
 (19) 
Solve for R. To disregard the nonreal solutions, use the RealDomain package.
 (20) 
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.
 (21) 
 (22) 
The result is the radius in kilometers (km) of a geostationary orbit.



and the Package


Although ScientificErrorAnalysis and ScientificConstants are separate packages, there are many connections between them.
One connection, for example, is that ScientificConstants[GetError] uses the ScientificErrorAnalysis package to calculate the errors of derived physical constants.
For more information on the connections between the two packages, see the help page ScientificErrorAnalysis,SEAandSC.

Go to Maple Portal Maple Portal for Engineers
