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Rydberg Constant

Jose Miguel G. Elises1, Jesha Faye T. Librea

2, Anna Romina T. Mercado

3and Jasper Edward A. Orense

4

1Department of Mechanical Engineering, UP Diliman, Quezon City

2Department of Mining, Metallurgical and Materials Engineering, UP Diliman, Quezon City3Department of Mining, Metallurgical and Materials Engineering, UP Diliman, Quezon City

4Institute of Civil Engineering, UP Diliman, Quezon City

AbstractWavelength is the distance between two peaks of a wave. It can be directly

measured using spectrometers like handheld spectrometer and it can also be

calculated using the equation of Max Planck. In the experiment, both

methods were used to determine the wavelength of five different colors of

LED lights (red, orange, green, blue, and violet). The results showed that the

wavelengths calculated from using the turn-on voltage value only had at most

12.75% discrepancy with the theoretical values which were within the range

of wavelengths measure using handheld spectrometer. This showed the two

methods were consistent with each other.

Keywords: LEDs, Turn-on voltage, Spectrometer, Wavelength

1. Introduction

In 1864, Scottish physicist James Clerk Maxwell published a paper that theorized that light is anelectromagnetic wave. He developed mathematical equations, called Maxwells equations, which defined the

behavior of light [1]. Light as an electromagnetic wave means that it has properties of a simple wave such as

amplitude, period, frequency, speed, and, the focus of this study: wavelength. The wavelength is a measure of

the distance between two peaks of a wave.

There is only a specific range of wavelength or frequency that humans can perceive. This is called the

visible spectrum, as shown in Figure 1. It lies from 400 nm to 700 nm of the whole electromagnetic spectrum[3].

Figure 1. Visible spectrum

One way to know the wavelength emitted by a light source is through measuring it using a

spectrometer. The basic function of a spectrometer is to take in light and break it into its spectral components to

produce spectral lines and to be able to measure the lights wavelength and/or the intensity [4]. An example of aspectrometer is the handheld spectrometer.

Another way of determining the wavelength is through the use of the proportionality of the frequency

of radiation with the energy of radiation. Max Planck introduced this relationship as he characterized the

absorption and emission of light energy of atoms by the equation:

E = n h f (1)

where n is the quantum number, f is the frequency of the vibration of the molecule and h is Plancks constant,

4.135 x 10-15

eVs [5].An application of Equation (1) is the light-emitting diode (LED), a special type of semiconductor that

emits light when voltage is applied across it. It is characterized by a band gap between the conduction band and

the valence band, as shown in Figure 2.

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Figure 2. Diode Band Diagram

Negatively charged electrons in the conduction band require a minimum voltage, Vo, or the turn-on

voltage, to move across the band-gap to the valence band, which contains positive charge carriers known as

holes. The voltage corresponds to the band energy, defined by:

e Vo= Eband energy (2)

wheree is the charge of the electron. The combination of electrons and the holes leads to an emission of light

[6].

Combining Equation (2) with Equation (1) and since the frequency of light, f, is the speed of light, c,divided by the wavelength, , Equation (1) can be rewritten as:

(3)

Therefore, by finding the turn-on voltage of the light source, using Equation (3), its wavelength may be

determined.

The objective of this study was to find the wavelength of different LEDs: red, orange, green, blue, and

violet, through two methods: (1) through the determination of the turn-on voltages of each LED and (2) the useof a handheld spectrometer. It aimed to compare the experimental data gathered from each.

From this study, it can be deduced if the results from the two methods were consistent with each other.

Also, through using the handheld spectrometer, the spectra found may be used as future references, as each

spectrum can be used to identify a corresponding type of LED.

2. Methodology

3. Results and Discussion

In the experiment, the different current-voltage readings of the LEDs were obtained and tabulated in

Tables 1. The current and voltage readings of each diode were plotted to form an IV curve which can be found

on Figures 1 to 5.

Table 1.Current-voltage readings of the different LEDs.

Red Orange Green Blue Violet

Current

(mA)

Voltage

(V)

Current

(mA)

Voltage

(V)

Current

(mA)

Voltage

(V)

Current

(mA)

Voltage

(V)

Current

(mA)

Voltage

(V)

0 1.53 0 1.55 0 1.8 0 2.23 0 2.57

0.001 1.71 0.001 1.75 0.004 1.92 0.001 2.51 0.002 2.91

0.002 1.78 0.002 1.82 0.037 2.1 0.002 2.61 0.004 3.03

0.003 1.81 0.003 1.85 0.077 2.15 0.003 2.66 0.012 3.18

0.004 1.83 0.004 1.86 0.137 2.19 0.004 2.7 0.024 3.31

0.005 1.85 0.005 1.88 0.037 3.5

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Figure 1. IV curve of the red LED in mA and V. Figure 2. IV curve of the orange LED in mA and V.

Figure 3. IV curve of the green LED in mA and V. Figure 4. IV curve of the blue LED in

mA and V.

Figure 5. IV curve of the violet LED in mA and V.

The best-fit equation of the linear portion of each of the IV curves was obtained using linear regression

and the corresponding x-intercept of each equation was calculated.The calculated x-intercept for each IV curve

would be equal to the turn-on voltage of the LED.

The frequency of each LED was obtained using the equation, f=V/h, and the corresponding wavelength

was calculated using the Equation, =c/f. The calculated turn -on voltage, frequency and wavelengths for each

LED were tabulated in Table 2, along with the theoretical values and the percent deviation.

Table 2.Experimental data of the turn-on voltage, frequency and wavelength together with the theoretical value

and its percent deviation of the different LEDs.

LED

TOV

(V) Frequency (Hz) Wavelength (m) Theoretical Wavelength (m) % Deviation

Red 1.75 4.23E+14 709.22 6.33E-07 12%

Orange 1.8 4.35E+14 689.66 6.12E-07 12.75%

y = 0.05x - 0.0875

R = 1

0

0.001

0.002

0.003

0.004

0.005

0.006

0 0.5 1 1.5 2Voltage (V)

I-V Curve of the Red LED

y = 0.0643x - 0.1158

R = 0.9643

0

0.001

0.0020.003

0.004

0.005

0.006

0 0.5 1 1.5 2

Voltage (V)

I-V Curve of the Orange LED

y = 1.0984x - 2.2741

R = 0.9683

0

0.03

0.06

0.09

0.120.15

0 0.5 1 1.5 2 2.5

Voltage (V)

I-V Curve of the Green LED

y = 0.0221x - 0.0558

R = 0.9959

0

0.001

0.002

0.003

0.0040.005

0 1 2 3

Voltage (V)

I-V Curve of the Blue LED

y = 0.0774x - 0.2335

R = 0.9928

0

0.01

0.02

0.03

0.04

0 1 2 3 4Voltage (V)

I-V Curve of the Violet LED

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Green 2.07 5.01E+14 598.80 5.34E-07 12.17%

Blue 2.52 6.09E+14 492.61 4.59E-07 7.41%

Violet 3.02 7.30E+14 410.95 4.04E-07 1.98%

The theoretical value of the wavelength used in the experiment was only based on the distinct color of

the LED. LEDs had wide range of wavelength values and its distinct color was based on the wavelength withthe highest intensity. So in order to verify the theoretical used to assess the experimental data gathered, another

experiment was done using handheld spectrometer. The ranges of wavelength of the LEDs seen on the

handheld spectrometer were tabulated on Table 3.

Table 3. Wavelength range of the different LED using the handheld spectrometer

Handheld Spectrometer

LED Wavelength Range (nm)

Red 580-670

Orange 570-700

Green 450-650

Blue 430-650

Violet 400-710

Based from the results obtained from the experiment, the IV curves obtained in the experiment were

very similar to the theoretical IV curves where it the graphs start exponentially but approaches linearity as the

voltage increases. It can also be observed that the obtained turn-on voltage, frequencies and wavelengths were

consistent to the theoretical values having the same linear trend. The turn-on voltage and the frequency also had

an inverse relationship with the wavelength. On the other hand, the experimental values of the wavelengths hada percent deviation that ranges from 1.98% for the violet LED up to 12.75% for the orange LED. This shows

that although the experiment was done successfully, errors were still present and this affected experimental

wavelength values and caused the 12.75% deviation. Finally, the comparison between the theoretical values of

the wavelength and the values obtained using a handheld spectrometer tells us that both methods can be used in

obtaining the wavelengths of different light sources, although handheld spectrometer only gives ranges, sincethe theoretical values of wavelengths are within the range of wavelength that the spectrometer gives. This alsomeans that the experimental data obtained were also consistent with spectrometer data except for the red LED

that had experimental wavelength not within the range. The discrepancy in the results may be caused by

personal and experimental errors like fluctuating power supply and the varying current and voltage values.

4. ConclusionIn conclusion, the experiment was able to achieve its objectives. The wavelengths of five LED lights (red,

orange, green, blue and violet) were both measured from the computation of the turn-on voltage and from the

handheld spectrometer. For the computation of the wavelength from the turn-on voltage of the LEDs, it was

observed that the experimental values followed the trend of the theoretical values and only showed a

discrepancy of not more than 12.75%. Then, using handheld spectrometer, the theoretical values of LEDs used

to assess the computed wavelengths were within its respective range of wavelengths. This showed that that the

wavelength computed from the turn-on voltage was consistent with what was seen in the handheld spectrometer.

References1. Myers, R. L. (2006). Light and Optics. The basics of physics(). Westport, Conn.: Greenwood Press.

2. "Properties of waves."Properties of waves.N.p., 29 Sept. 1999. Web. 9 May 2014.

.

3. Seeds, Michael A., and Dana Backman. "Light and Telescopes."Foundations of astronomy. 1990 ed.

Belmont, Calif.: Wadsworth Pub. Co., 1990. . Print.

4. "How Does a Spectrometer Work?."BW Tek. B&W Tek, Inc., 1 Jan. 2014. Web. 9 May 2014.

.

5. O'Connor, Leah R., O'Connor, Patrick J., "Measuring Planck's Constant Using a Light Emitting Diode." The

Physics Teacher, pp 423-425, 1974.

6.

Dubson, Micheal A., Taylor, John R., Zafiratos, Chris D.,Modern Physics for Scientists and Engineers,Prentice Hall, 2003.

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