**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 H

_{2}, O_{2}, 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.

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