PHYSICS PROJECT ON
MEASUREMENT OF PLANCK’S CONSTANT THROUGH “KNEE VOLTAGE” OF LEDs NAME :- Ishaan Arora CLASS :- XII SCIENCE BOARD ROLL :Page
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CERTIFICATE THIS IS TO CERTIFY THAT I ISHAAN ARORA OF CLASS 12TH SCIENCE HAS SATISFACTORILY COMPLETED PHYSICS PROJECT TITLED “ MEASUREMENT OF PLANCK’S CONSTANT USING LIGHT-EMITTING DIODES THROUGH KNEE VOLTAGE ” DURING THE ACADEMIC SESSION 2017-18 UNDER THE SUPERVISION OF MR. UDAY KANT ROY.
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TEACHER’S SIGNATURE :DATE :-
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ACKNOWLEDGEMENT
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I ISHAAN ARORA WISH TO EXPRESS MY GRATITUDE AND SINCERE THANKS TO MY PHYSICS LAB ASSISTANT MR. SURESH UNDER THE GUIDANCE OF MY PHYSICS TEACHER MR. UDAY KANT ROY FOR THE COMPLETION OF THE PROJECT.
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CONTENTS
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Introduction History Advantages & Disadvantages Applications Aim Apparatus Required Theory Procedure Observation Conclusion Precautions Bibliography
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INTRODUCTION LED (Light Emitting Diode) Electronic Symbol :-
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Light Emitting Diodes (LED’s) convert electrical energy into light energy. They emit radiation (photons) of visible wavelengths when they are “forward biased”. This is caused by electrons from the “n” region in the LED giving up light as they fall into holes in the “p” region. This effect is called electroluminescence and the color of the light (corresponding to the energy of photon) is determined by energy gap of the Semiconductor.
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HISTORY LED Invented by: Nick Holonyak Jr. (1962) Electroluminescence as a phenomenon was discovered in 1907 by the British experimenter H. J. Round of Marconi Labs, using a crystal of silicon carbide and a cat's-whisker detector. Russian inventor Oleg Losev reported creation of the first LED in 1927. His research was distributed in Soviet, German and British scientific journals, but no practical use was made of the discovery for several decades. Kurt Lehovec, Carl Accardo, and Edward Jamgochian explained these first light-emitting diodes in 1951 using an apparatus employing SiC crystals with a current source of battery or pulse generator and with a comparison to a variant, pure, crystal in 1953. The first visible-spectrum (red) LED was developed in 1962 by Nick Holonyak, Jr. while working at General Electric M. George Craford, a former graduate student of Holonyak, invented the first yellow LED and improved the brightness of red and red-orange LEDs
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An Old LED
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The Planck’s constant (denoted h) is a physical constant that is the quantum of action. First recognized in 1900 by Max Planck.
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ADVANTAGES & DISADVANTAGES ADVANTAGES
Very low voltage and current are enough to drive the LED. Voltage range – 1 to 2 volts. Current – 5 to 20 milliamperes. The response time is very less – only about 10 nanoseconds. The device does not need any heating and warm up time. Miniature in size and hence light weight. An LED has a life span of more than 20 years. DISADVANTAGES
The temperature depends on the radiant output power and wavelength.
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A slight excess in voltage or current can damage the device. The device is known to have a much wider bandwidth compared to the laser. Page
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APPLICATIONS Indicators and signs Large-area LED displays are used as stadium displays, dynamic decorative displays, and dynamic message signs on freeways. Thin, lightweight message displays are used at airports and railway stations, and as destination displays for trains and buses. Lighting LEDs are used as street lights. They are also used in handheld devices such as flashlights. LED strobe lights or camera flashes
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Other applications The LEDs are used extensively in optical fiber and free space optics communications. This includes remote controls, such as for TVs, VCRs, and LED
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Data communication and other signaling
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Computers, where infrared LEDs are often used Efficiency
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AIM
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To measure Planck’s constant using lightemitting diodes using “Knee voltage”.
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APPARATUS REQUIRED
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0-10 V power supply. One-way key Rheostat Ammeter Voltmeter 1 K resistor Different known wavelength LED’s (Light-Emitting Diodes)
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THEORY an LED
Like a normal diode, the LED consists of a chip of semiconducting material doped with impurities to create a p-n junction. As in other diodes, current flows easily from the p-side, or anode, to the n-side, or cathode, but not in the reverse direction. Chargecarriers—electrons and holes—flow into the junction from electrodes with different voltages. When an electron meets a hole, it falls into a lower energy level and releases energy in the form of a photon.
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The wavelength of the light emitted, and thus its colour, depends on the band gap energy of the materials forming the p-n junction. The materials used for the LED have a direct band gap with energies corresponding to near-infrared, visible, or nearultraviolet light.
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The following table shows the available colours with wavelength range, voltage drop, and material:
Colour Wavelength [nm]
Voltage drop [ΔV]
Semiconductor material
ΔV < 1.63
Gallium arsenide (GaAs) Aluminium gallium arsenide (AlGaAs)
610 < λ < 760
1.63 < ΔV < 2.03
Aluminium gallium arsenide (AlGaAs) Gallium arsenide phosphide (GaAsP)
Orange 590 < λ < 610
2.03 < ΔV < 2.10
Gallium arsenide phosphide (GaAsP) Gallium(III) phosphide (GaP)
2.10 < ΔV < 2.18
Gallium arsenide phosphide (GaAsP) Aluminium gallium indium phosphide (AlGaInP)
Infrared λ > 760
Red
Yellow
570 < λ < 590
500 < λ < 570
1.9 < ΔV < 4.0
Blue
450 < λ < 500
2.48 < ΔV < 3.7
Zinc selenide (ZnSe)
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Green
Traditional green: Gallium(III) phosphide (GaP) Pure green: Indium gallium nitride (InGaN)
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An LED is a two-terminal semiconductor light source. In the unbiased condition a potential barrier is developed across the p-n junction of the LED. When we connect the LED to an external voltage in the forward biased direction, the height of potential barrier across the p-n junction is reduced. At a particular voltage the height of potential barrier becomes very low and the LED starts glowing, i.e., in the forward biased condition electrons crossing the junction are excited, and when they return to their normal state, energy is emitted. This particular voltage is called the knee voltage or the threshold voltage. Once the knee voltage is reached, the current may increase but the voltage does not change. The light energy emitted during forward biasing is given as,
E=
hc λ
(1)
where c - Velocity of light. h - Planck’s constant. λ - Wavelength of light. If V0 is the forward voltage applied across the LED when it begins to emit light (the knee voltage), the energy given to electrons crossing the junction is,
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Equating (1) and (2), we get
(2) Page
𝐸 = e𝑉0
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𝑒𝑉0
=
ℎ𝑐 𝜆
(3)
The knee voltage V0 can be measured for LED’s with different values of λ (wavelength of light).
𝑉0 =
hc 1 e
() λ
(4)
Now from equation (4), we see that the slope s of a 1 graph of V0 on the vertical axis vs on the horizontal λ
axis is
𝑠=
ℎ𝑐 𝑒
(5)
To determine Planck’s constant h, we take the slope s from our graph and calculate 𝑒 𝑐
ℎ= 𝑠 Using the known value 𝑒 𝑐
= 5.33 × 10−28 𝐶𝑠𝑚−1
Alternatively, we can write equation (3) as e c
h = λ𝑉0
(6)
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and calculate h for each LED, and take the average of our results.
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PROCEDURE 1. Make connections as shown in the circuit diagram. 2. 3.
Insert the key to start the experiment.
Adjust the rheostat value till the LED starts glowing, or in the case of the IR diode, whose light is not visible, until the ammeter indicates that current has begun to increase.
4. Corresponding voltage across the LED is measured using a voltmeter, which is the knee voltage. 5. Repeat, by changing the LED and note down the corresponding knee voltage.
6.
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Using the formula given and slope of graph find the value of the Planck's constant.
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OBSERVATION From Equation 𝒆 Colour Wavelengt No. of Knee 𝒉 = 𝝀𝑽 𝒄 of LED h divisions in voltage Voltmeter (Kgm2s-1) 𝒏𝒎/ (𝑽𝟎 ) ( −𝟗 ) 𝟏𝟎 𝒎 (n) (L.C. X n)
Red
630
38
1.9
Yellow
590
44
2.2
Green
510
48
2.4
Blue
470
52
2.6
6.568 x 10-34 6.605 x 10-34 6.552 x 10-34 6.565 x 10-34
CALCULATION Least count of Voltmeter = 0.05 V Mean value of Planck’s constant =
= 6.572 x 10-34 Kgm2s-1
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(6.568 x 10-34) +(6.552 x 10-34) +(6.565 x 10-34)+(6.605 x 10-34)
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From Graph V0 vs 1/λ
3
2.5
2.6
Blue
2.4
V0
2 1.5
Green
2.2
Yellow
1.9
Red
1 0.5 0 1587301.59
1694915.25
1960784.31
2127659.57
1/λ
CALCULATION Slope from graph (S) = 1.75 X 10-6 Value of Planck’s constant ( ℎ =
𝑒 𝑠 𝑐
)
𝑒 = 5.33 × 10−28 [𝑐 ] 𝑠 = 1.75 × 10−6
ℎ = 5.33 × 10−28 × 1.75 × 10−6
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= 6.266 x 10-34 Kgm2s-1
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CONCLUSION
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The actual (theoretical) value of Planck’s constant is 6.626 x10-34 Kgm2s-1 and the values in the above experiment are precise as well as in the close conformity with the actual value of the Planck’s constant.
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BIBLIOGRAPHY Following websites and books served as a source for my project: -
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https://www.google.co.in
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https://www.wikipedia.org
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http://vlab.amrita.edu
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https://www.shutterstock.com (CREDIT: Images)
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New Simplified Physics
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A. S.L. Arora
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