HP Prime: Diatomic Molecules

HP Prime: Diatomic Molecules

Diatomic Molecules

The program DIATOMIC will calculate:

*  Distance from the center of mass for each molecule

*  Inertia of the molecule

*  Rotational Energy at level j  (j = 0, 1, 2, 3…)

*  Vibrational Energy at level n  (n = 0, 1, 2, 3…)

A diatomic molecule is a molecule made of two atoms.  Examples are H₂, O₂, NaCl (sodium chloride), and CO (carbon monoxide). 

Input:

*  Mass of the two molecules, in atomic mass units (u).  The program will convert them to kilograms.  The conversion is 1 u ≈ 1.660538921 * 10^-27 kg

*  Distance of the “bar” between the two molecules.  Give this in ångströms, which an ångström is 10^-10 m. 

*  Rotational and Vibrational Energy levels.  They do not have to be the same.

*  Frequency of the diatomic molecule in 10^12 Hz.  Typically, molecules and atoms exhibit frequencies in the order of 10^13 Hz.

The formulas are derived from the use of the Schrödinger Equation.  While I won’t give much details, a derivation can be found in many resources, such as this link:  http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Rotational_Spectroscopy/Rotational_Spectroscopy_of_Diatomic_Molecules. 

This program can be adopted to other graphing calculators, but here is a version for the HP Prime:

Program DIATOMIC

EXPORT DIATOMIC()

BEGIN

// EWS 2015-07-09

// Diatomic Molecule

LOCAL m1,m2,r,l1,l2,I;

LOCAL j,n,w;

LOCAL Er,Ev;

// Input

INPUT({m1,m2,r,j,n,w},

"Diatomic Molecule",

{"Mass 1:","Mass 2:",

"r:","J:","N:","freq:"},

{"Mass in atomic units",

"Mass in atomic units",

"Distance in Angstroms",

"Rotational energy level",

"Vibration energy level",

"Frequency (10^12 Hz)"});

// Integer Parts

n:=IP(n);

j:=IP(j);

// Convert to kg

m1:=m1*1.660538921ᴇ−27;

m2:=m2*1.660538921ᴇ−27;

// Convert Angstroms to m;

r:=r/1ᴇ10;

// Convert to Hz;

w:=w*1ᴇ12;

// Lengths

l1:=m2*r/(m1+m2);

l2:=m1*r/(m1+m2);

// Inertia:

I:=m1*l1^2+m2*l2^2;

// Rotational Energy:

Er:=1.054571726ᴇ−34^2/(2*I)*j*(j+1);

// Vibrational Energy:

Ev:=(n+1/2)*1.054571726ᴇ−34*w;

// Results

PRINT();

PRINT("Distance to Center (m):");

PRINT("From Mol. 1: "+STRING(l1));

PRINT("From Mol. 2: "+STRING(l2));

PRINT("Inertia:");

PRINT(STRING(I)+" kg m^2");

PRINT("Rotational Energy:");

PRINT(STRING(Er)+" J");

PRINT("Vibrational Energy:");

PRINT(STRING(Ev)+" J");

RETURN({l1,l2,I,Er,Ev});

  

END;

  

Example

Mass 1:  Hydrogen:  1.00794 u

Mass 2:  Chlorine:  35.4270 u

Distance:  6 ångströms

Frequency:  3.6 x 10^13 Hz

Input Screen:

Output Screen:

Energy:

Rotational:  approx. 1.90*10^-23 J

Vibration:  approx. 5.69*10^-21 J

Sources:

Strong, Benjamin.  “Rotational Spectroscopy of Diatomic Molecules”  http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Rotational_Spectroscopy/Rotational_Spectroscopy_of_Diatomic_Molecules   March 26, 2015.   Retrieved July 5, 2015.

Wikipedia.  “Atom Vibrations”  https://en.wikipedia.org/wiki/Atom_vibrations  Retrieved July 9, 2015.

Young, Hugh D. & Roger A Freedman   “University Physics with Modern Physics”  11^th Ed.  Pearson:  San Francisco.  2003

  

Eddie

This blog is property of Edward Shore.  2015.