DuckieDai Quantum Wavelength and Hydrogenic Transitions Python Program

chemistry · MIT License

Overview

Calculate de Broglie wavelength or momentum, a nonrelativistic electron wavelength, and hydrogenic Rydberg wavelengths and transition information.

Not calculator tested
Downloaded 34 times
Version 1.0.0
2716 bytes
Uses math

Download dWAVE.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer is the intended path; calculator OS, Python App, transfer, and execution have not yet been tested for this release
p = m*v and the voltage relation are nonrelativistic.
The Rydberg modes apply to hydrogen and one-electron hydrogen-like ions using the stated constant.
Physical magnitudes and quantum numbers are positive; transition levels must differ; the emission-only mode requires upper n greater than lower n.

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Learn the math

How de Broglie wavelength and hydrogen transitions work

The idea

Moving particles behave like waves, with a wavelength that gets shorter as momentum rises. For everyday objects the wavelength is far too small to notice; for electrons it is comparable to the size of an atom.

Electrons in a hydrogen-like atom can only have certain energies. Jumping between levels emits or absorbs light of a specific wavelength, given by the Rydberg formula.

The formula

lambda = h/(m*v) = h/p

1/lambda = R*Z^2*(1/n1^2 - 1/n2^2)

lambda: wavelength
h: Planck's constant, 6.626 x 10^-34 J*s, built in
m, v, p: mass (kg), velocity (m/s), and momentum (kg*m/s)
n1, n2: the lower and upper energy levels

Using the program

1 finds a wavelength from mass and velocity. 2 finds it from momentum. 3 finds momentum from a wavelength.
4 finds an electron's wavelength from an accelerating voltage.
5 finds the wavelength of a hydrogen-like transition. 6 describes the transition.

Worked example

An electron (9.109 x 10^-31 kg) moves at 2.2 x 10^6 m/s. Choose 1 and enter 9.109e-31 and 2.2e6.

lambda = 6.626e-34/(9.109e-31 x 2.2e6)

The program shows lambda nm = 0.3306 (it prints more decimal places), about the size of an atom.

Tips and common mistakes

Type powers of ten with e: 9.109e-31.
The electron-voltage mode ignores relativity, so it is for modest voltages.
Dropping from a high level to a low one emits light; going up absorbs it.

Where this comes up

It covers the atomic structure and quantum unit of general chemistry and the modern physics unit of physics: line spectra, the Bohr model, and matter waves.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

from math import sqrt

h=6.62607015e-34
light=299792458
me=9.1093837e-31
charge=1.602176634e-19
R=1.0973731568e7

def duckiedai_intro(program_name,wait=True):
 title=program_name[:16]
 empty=16-len(title)
 left=empty//2
 right=empty-left
 print("+----------------------+")
 print("|   "+" "*left+title+" "*right+"   |")
 print("|                      |")
 print("|       __             |")
 print("|   ___(o )>  quack!   |")
 print("|   \\ <_. )           |")
 print("|    `---'             |")
 print("|     by DuckieDai     |")
 print("+----------------------+")
 print("Loading...")
 if wait:
  input("Press enter to start ")
  print("\n"*6)

def pos(s):
 while 1:
  try:
   x=float(input(s))
   if x>0:return x
  except:pass
  print("Enter a positive #")

def whole(s):
 while 1:
  try:
   x=int(input(s))
   if x>0:return x
  except:pass
  print("Enter a whole #")

def menu(s,top):
 while 1:
  try:
   x=int(input(s))
   if x>0 and x<=top:return x
  except:pass
  print("Invalid choice")

def wave(w):
 print("lambda m =",w)
 print("lambda nm =",w*1e9)
 print("lambda pm =",w*1e12)

def photon(w):
 f=light/w
 e=h*f
 print("Frequency Hz =",f)
 print("Energy J =",e)
 print("Energy eV =",e/charge)

duckiedai_intro("QUANTUM WAVE")
print("QUANTUM WAVELENGTH")
print("1 lambda from m,v")
print("2 lambda from p")
print("3 Find momentum")
print("4 Electron voltage")
print("5 Rydberg lambda")
print("6 Transition info")
c=menu("Choose 1-6: ",6)

if c==1:
 m=pos("Mass kg: ")
 v=pos("Velocity m/s: ")
 p=m*v
 wave(h/p)
 print("p kg*m/s =",p)

elif c==2:
 p=pos("Momentum kg*m/s: ")
 wave(h/p)

elif c==3:
 print("1 meters 2 nm 3 pm")
 u=menu("Choose unit: ",3)
 w=pos("lambda: ")
 if u==2:w=w*1e-9
 elif u==3:w=w*1e-12
 print("p kg*m/s =",h/w)

elif c==4:
 v=pos("Voltage V: ")
 p=sqrt(2*me*charge*v)
 wave(h/p)
 print("p kg*m/s =",p)
 if v>10000:print("High V: relativity matters")

elif c==5:
 z=whole("Atomic Z: ")
 n1=whole("Lower n1: ")
 n2=whole("Upper n2: ")
 if n2<=n1:print("n2 must exceed n1")
 else:
  w=1/(R*z**2*(1/n1**2-1/n2**2))
  wave(w)
  photon(w)

else:
 z=whole("Atomic Z: ")
 n1=whole("Initial n: ")
 n2=whole("Final n: ")
 if n1==n2:print("No transition")
 else:
  w=1/(R*z**2*abs(1/n2**2-1/n1**2))
  if n1>n2:print("EMISSION")
  else:print("ABSORPTION")
  print("n",n1,"to",n2)
  wave(w)
  photon(w)
  if z==1:
   low=min(n1,n2)
   if low==1:print("Lyman: UV")
   elif low==2:print("Balmer: visible")
   elif low==3:print("Paschen: infrared")
   else:print("Higher H series")

input("ENTER for guide: ")
print("QUICK GUIDE")
print("lambda=h/p")
print("More p: shorter lambda")
print("High n to low n: emit")
print("Low n to high n: absorb")
print("DuckieDai: done!")
input("ENTER to exit: ")

from math import sqrt
h=6.62607015e-34
light=299792458
me=9.1093837e-31
charge=1.602176634e-19
R=1.0973731568e7
def duckiedai_intro(program_name,wait=True):
title=program_name[:16]
empty=16-len(title)
left=empty//2
right=empty-left
print("+----------------------+")
print("| "+" "*left+title+" "*right+" |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n"*6)
def pos(s):
while 1:
try:
x=float(input(s))
if x>0:return x
except:pass
print("Enter a positive #")
def whole(s):
while 1:
try:
x=int(input(s))
if x>0:return x
except:pass
print("Enter a whole #")
def menu(s,top):
while 1:
try:
x=int(input(s))
if x>0 and x<=top:return x
except:pass
print("Invalid choice")
def wave(w):
print("lambda m =",w)
print("lambda nm =",w*1e9)
print("lambda pm =",w*1e12)
def photon(w):
f=light/w
e=h*f
print("Frequency Hz =",f)
print("Energy J =",e)
print("Energy eV =",e/charge)
duckiedai_intro("QUANTUM WAVE")
print("QUANTUM WAVELENGTH")
print("1 lambda from m,v")
print("2 lambda from p")
print("3 Find momentum")
print("4 Electron voltage")
print("5 Rydberg lambda")
print("6 Transition info")
c=menu("Choose 1-6: ",6)
if c==1:
m=pos("Mass kg: ")
v=pos("Velocity m/s: ")
p=m*v
wave(h/p)
print("p kg*m/s =",p)
elif c==2:
p=pos("Momentum kg*m/s: ")
wave(h/p)
elif c==3:
print("1 meters 2 nm 3 pm")
u=menu("Choose unit: ",3)
w=pos("lambda: ")
if u==2:w=w*1e-9
elif u==3:w=w*1e-12
print("p kg*m/s =",h/w)
elif c==4:
v=pos("Voltage V: ")
p=sqrt(2*me*charge*v)
wave(h/p)
print("p kg*m/s =",p)
if v>10000:print("High V: relativity matters")
elif c==5:
z=whole("Atomic Z: ")
n1=whole("Lower n1: ")
n2=whole("Upper n2: ")
if n2<=n1:print("n2 must exceed n1")
else:
w=1/(R*z**2*(1/n1**2-1/n2**2))
wave(w)
photon(w)
else:
z=whole("Atomic Z: ")
n1=whole("Initial n: ")
n2=whole("Final n: ")
if n1==n2:print("No transition")
else:
w=1/(R*z**2*abs(1/n2**2-1/n1**2))
if n1>n2:print("EMISSION")
else:print("ABSORPTION")
print("n",n1,"to",n2)
wave(w)
photon(w)
if z==1:
low=min(n1,n2)
if low==1:print("Lyman: UV")
elif low==2:print("Balmer: visible")
elif low==3:print("Paschen: infrared")
else:print("Higher H series")
input("ENTER for guide: ")
print("QUICK GUIDE")
print("lambda=h/p")
print("More p: shorter lambda")
print("High n to low n: emit")
print("Low n to high n: absorb")
print("DuckieDai: done!")
input("ENTER to exit: ")

Filename: dWAVE.py
Size: 2716 bytes
SHA-256: 8238d675998a4041554d4d58d2c8d3641dc07972c2f8b7a6287494f809419f0a

Usage

Inputs

Mass and speed, momentum, wavelength, or electron accelerating voltage
Atomic number and principal quantum levels for hydrogenic transitions

Outputs

Wavelength in metres, nanometres, and picometres
Momentum; or transition direction, photon frequency, and photon energy

Units: SI units are used for mass, speed, momentum, voltage, wavelength, frequency, and energy; entered nm or pm are explicitly converted.

Assumptions and limitations

Assumptions

p = m*v and the voltage relation are nonrelativistic.
The Rydberg modes apply to hydrogen and one-electron hydrogen-like ions using the stated constant.

Constraints

Physical magnitudes and quantum numbers are positive; transition levels must differ; the emission-only mode requires upper n greater than lower n.

Known failures

Multi-electron atoms are not described by the Z-squared hydrogenic formula.
High accelerating voltage requires a relativistic wavelength correction.

Compatibility and review

Review status: Not calculator tested
Tested on: The owner reports personally testing the supplied archive programs on a calculator; exact model, OS, and Python App versions were not recorded
What happened: Owner reported interactive testing is disclosed, but the published bytes are not labeled independently calculator tested because the environment is unrecorded and Arrhenius received a narrow intake correction
Dependencies: math
Suggested calculator name: DWAVE — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as DWAVE or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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