Modeling Bohr’s Quantum Theory of H-Atom for …Presentation by G. Singh at MCC 4/7/2014...

Modeling Bohr’s Quantum Theory of H-Atom

for STEM Education in Virtual Lab

Gurmukh Singh, PhD

Department of Computer and Information Sciences

SUNY at Fredonia, Fredonia, NY 14063

[email protected]

Advancing What Works in STEM Education

PKAL Upstate New York Regional Network

Improving Learning in Undergraduate STEM

Monroe Community College, Rochester, NY

April 5, 2014

mailto:[email protected]

2

Visual Studio.NET and MS Excel for STEM

• MS Visual Studio.NET 2012 and Excel 2010 are often used

software system for undergraduate and graduate teaching

in colleges, scientific labs, private companies, and

businesses in the US [1, 2, 3]

• Usually MS Visual Studio.NET and Excel are licensed and

installed on college and university microcomputers

• Student user or an instructor does not have to shell out

extra money to purchase them

• Instructors, students and researchers have an easy access

to these two software systems in their educational/research

institutes

Presentation by G. Singh at MCC

Rochester, NY, April 05, 2014 4/7/2014


Rochester, NY, April 05, 2014 3

• MS Visual Studio.NET 2012 and Excel 2010 are quite

useful software systems with user friendly Graphical User

Interface (GUI)

• These two software systems have unique advantage and

ability to simulate data for any science, technology,

engineering and mathematical (STEM) problem

• Both software systems make any experimentally collected

or theoretical simulated data in useful graphical form for

the targeted audience of STEM students, instructors and

scientists in several areas of chemistry, physics, biology,

engineering science, biology, mathematics, bioinformatics,

information systems and computer science etc.

4/7/2014

Visual Studio.NET and MS Excel for STEM

Brief Review of Nature of Waves

4/7/2014



Properties of waves

1. Wind-generated ocean or earthquake waves: frequency, ν = 5-

20 Hz, wavelength, λ = 100-200 m

2. Tsunami-generated waves: frequency, ν = 1.6-2 Hz, wavelength,

λ ≥ 500 km

3. Wave speed, v = λν (m/s): Speed of sound in air v = 332 m/s

All Electromagnetic Waves Including X-rays, UV, Visible,

Infrared, AM & FM Radio Waves, Microwaves etc.

-Do not require a medium to travel

-Travel at constant speed, e.g., speed of light in vacuum, c = 3.0 ᵡ

106 m/s

4/7/2014



Quantized Energy and Light Photons

Max Planck (1858-1947) Proposal: Emission and absorption

of radiation by a black body or an atom takes place only in

discrete amounts called quanta, i.e., energy is quantized:

"A new scientific truth does not triumph by convincing its

opponents and making them see the light, but rather because

its opponents eventually die, and a new generation grows up

that is familiar with it.“ Max Planck, A Scientific Autobiography

and Other Papers , 1949

DE = hn,

where DE = energy difference between two states, h= Plank’s

constant andn = frequency of emitted or absorbed radiation

4/7/2014



Quantization and Particle Nature of Light

Common analogy to explain quantization: Consider walking

up a ramp (continuous) versus walking up stairs in steps

So, energy is always emitted or absorbed in whole-number,

multiples of photon energy, hn

4/7/2014



First Experimental Evidence of Quantization:

Photoelectric Effect and Photons (Einstein, 1905)

Max Planck 1918 Nobel Prize

in physics for quantum theory

Albert Einstein’s 1921 Nobel Prize

in physics for photoelectric effect

4/7/2014



Thus, if light photons of discrete energy or frequency fall

on surface of a metal, electrons may be ejected from that

metal. This is called photo-electric effect

1. The electrons will only be ejected if the frequency of

incident light radiation is greater than a certain minimum

frequency (threshold frequency). Below the threshold

frequency, no electrons are ejected

2. Above the threshold frequency, number of electrons

ejected increases as the intensity of incident light

increases but not the energy of emitted electrons

3. Kinetic energy of emitted electrons increases as the

frequency of incident light radiation increases

4/7/2014



Implications of Photo-Electric Effect

Beam of light

Einstein’s Explanation of Photo-Electric Effect

Energy is quantized; each quantum called a photon

Energy of each quantum given by Planck’s equation:

Minimum energy required to release an electron from metal

is called the work function, wo of that metal.

4/7/2014



E = w = hn

Let wo = hno

If light did not have particle properties, then increasing

intensity of light should transfer enough energy to release

electron, e- (light would be a continuous energy stream),

according to classical electrodynamics.

If E < wo, i.e., if n < no, each photon does not have enough

energy to release an electron, and thus E = hn < hno

4/7/2014



Einstein’s Explanation of Photo-Electric Effect

Wave Nature of Light Explained Through A Single-

Slit Diffraction Experiment

4/7/2014



Light has a dual nature: (a) In certain experiments light

behaves as particles such as photo-electric effect, and (b) in

other experiments light can act as a wave just like diffraction

of light from a single slit as shown above or may a double-

slit experiment.

Line Spectra and Bohr’s Model

1. Monochromatic: Laser light is composed of a single wavelength,

λ or frequency, ν

2. Radiation that spans a discrete array of different wavelengths is

non-continuous or coherent

3. White light can be split up into a continuous spectrum of colors.

Max Planck (right) with Neils Bohr,

1922 Nobel Prize in physics.

4/7/2014



+Gas Discharge Tube With High Applied

Voltage at Both Ends

Simple gas like Na or H2

Emission spectrum is a line spectrum, not a

continuous spectrum

4/7/2014



Bohr’s discrete quantum states basis for H-atom model

Nucleus

Electrons confined to orbits of

specific radii called stationary

states, which are “allowed”

and do not permit electron to

freely spiral inward contrary to

classical electrodynamics

1. In a stationary state, e- orbits the nucleus without radiating energy

2. Between stationary states, electron, e- radiates energy as photons

(hv) until it makes transition to a new stationary state.

3. Therefore, an e- in an atom can have only particular energies!

4/7/2014

Presentation by G. Singh at MCC Rochester, NY,

April 05, 2014 15

n = 1

n = 2

n = 3

n = 4

n = ∞

The first orbit in the Bohr model has n = 1, closest to the

nucleus, and has negative energy by convention.

The outermost orbit in the Bohr model has n (quantum

number) close to infinity that corresponds to zero energy, i.e.,

the electron has escaped from the influence of the nucleus.

Energy = 0

Energy is

negative

Bohr’s discrete quantum states basis for H-atom model

4/7/2014

Presentation by G. Singh at MCC Rochester,

NY, April 05, 2014 16

-13.6193 eV

-3.4048 eV

-1.5132 eV

-0.8512 eV

n = 1

n = 2

n = 3

n = 4

n = ∞

Electrons in the Bohr model can only jump between states

by absorbing and emitting energy in quanta (hv).

This diagram shows emission of light quanta or light

photons of various energies or frequencies

Bohr’s discrete quantum states as basis for H-atom model

4/7/2014


NY, April 05, 2014 17

n = 1

n = 2

n = 3

n = 4

n = ∞

Electrons in the Bohr model can only jump between states

by absorbing and emitting energy in quanta (hν).

This diagram shows absorption of light quanta or light

photons of various energies or frequencies


4/7/2014


NY, April 05, 2014 18

Electrons in the Bohr model can only jump between orbits by absorbing and emitting energy in quanta (hν).

The amount of energy absorbed or emitted on transition between states is given by DE = Ef - Ei

n = 1

n = 2

n = 3

n = 4

n = ∞


4/7/2014


NY, April 05, 2014

Lyman series

Balmer series

Paschen series

19

n = 1

n = 2

n = 3

n = 4

n = ∞

Actual line spectrum of Sodium, Na and Hydrogen, H atoms

DE = Ef – Ei = hv

4/7/2014


NY, April 05, 2014 20

1. To calculate the wavelengths of the spectral lines of the

H-atom, and Rydberg’s equation:

H

2 2

i f

R 1 1ν = -

h n n

2. Actual formula to compute wavelength of spectral lines

for H-atom was derived by Neils Bohr in 1913 using

postulates based on quantum theory:

=

2232

0

42 11

8

1

fi

e

nnch

eZm

4/7/2014



Actual Bohr’s Model Simulations

• To model Bohr’s quantum theory of hydrogen atom

for STEM education in a virtual lab [4]

• Performed simulations using two software systems

namely MS Excel 2010 and Visual Studio.NET 2012

• Can be done in a university classroom setting for

undergraduates and graduates of chemistry, physics,

engineering, mathematics, information systems and

computer science

• Plotted discrete energy level diagram for Lyman, Balmer,

Paschen, Brackett, Pfund and Humphreys series

• Compared the simulated results with experimentally

available data on H-atom in visible part of the

electromagnetic spectrum

MS Excel Built-in Logical Functions

4/7/2014



24

MS Excel 2010 Built-in Functions Used

24


Rochester, NY, April 05, 2014

• Logical function:

IF(logical_test, [value_if_true], [value_if_false])

AND(logical1, [logical2],…) AND returns a TRUE value if all arguments of the function

are TURE

• Pseudo-random number generating function:

RAND( )

• RAND( ) function could be used to generate any kind of

fractional pseudo-random number in a range between

0 and 1

• Performed more than 2000-5000 computer simulations

for the current presentation

4/7/2014

Screenshot of MS Excel Name Manager

4/7/2014



Screenshot of Visual Studio.NET 2012 GUI

4/7/2014



Screenshot of Visual Studio.NET Before Debug

4/7/2014



Screenshot of Visual Studio.NET After Debug

4/7/2014



Model Lyman

Series (nm)

Model Balmer

Series (nm)

Model Paschen

Series (nm)

Experimental

Balmer Series

(nm) [11]

λα 121.611 656.700 1876.287 656.285 (Red)

λβ 102.609 486.445 1282.618

486.133

(Blue-green)

λγ 97.289 434.326 1094.501 434.047 (Violet)

λδ 95.009 410.438 1005.573 410.174 (Violet)

λε 93.814 397.263 955.201 397.007(Violet)

λ∞ 91.208 364.834 820.876 -

nf = 2, 3, 4,…

→ ni = 1

nf = 3, 4, 5,…

→ ni = 2

nf = 4, 5, 6,… →

ni = 3

nf = 3, 4, 5,… →

ni = 2

Comparison of Bohr’s Quantum Model

and Experimental Results for H-atom

Concluding Remarks

We may conclude that current presentation has very

important implications for STEM students and instructors of

chemistry, physics, engineering, mathematics, information

systems and computer science and medical sciences:

• Students/instructors could learn how to employ software

systems such as MS VB Studio.NET 2012 [5] and MS Excel

2010 to simulate the basic concept of Bohr’s model of H-atom

• In chemistry, physics, engineering, mathematics, information

systems, computer science, students could visualize a real-

time application of this fundamental concept of natural

sciences in a virtual laboratory with latest version of MS Excel

2010 and .NET 2012.

Acknowledgements

I am really to grateful Dr. John Kijinski, Dean, College of

Liberal Arts and Sciences, SUNY at Fredonia for approving

and funding my visit to present my scholarly work at STEM

Meeting held at Monroe Community College, Rochester, NY. I

am thankful to Dr. Reneta Barneva, Professor and Chair,

Department of Computer and Information Sciences to provide

me with necessary facilities to conduct this research work.

Some of jpeg/png image files used in current presentation

are downloaded from wikipedia.com and author extends

thanks to this free source of images.

References

1. Microsoft Corporation, One Microsoft Way, Redmond, WA

98052-6399. For further information visit the website

http://www.microsoft.com/en/us/default.aspx

2. http://www.sun.com/;http://www.ibm.com/;

3. http://www.research.att.com/

4. R. Grauer and J. Scheeren, Microsoft Office, Excel 2010

(Comprehensive Ed), Prentice Hall Inc. (2010).

5. G. Singh, Computer Simulations of Quantum Theory of

Hydrogen Atom For Natural Science Education Students in

a Virtual Lab, J. Edu. Tech. Sys., Vol. 40 (3), 273-286

(2011-2012).











http://www.sun.com/;http:/www.ibm.com/















http://www.research.att.com/









http://www.cs.fredonia.edu/singh/BohrModel_VBStudio.pdf

































Any Questions Please?

Thank You For Your Time!

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Modeling Bohr’s Quantum Theory of H-Atom for …Presentation by G. Singh at MCC 4/7/2014...

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