Abstract
Optical spectroscopy studies the interaction between electromagnetic radiation and matter. Physicists use a spectrophotometer to determine specific wavelengths of absorption and emission for particular substances. This mechanism was created by August Beer in 1913, and later modernised by Arnold Beckman in 1940. Spectrophotometers provide astronomers with useful information particularly when using hydrogen (H) and helium (He) – the two elements stars mainly consist of. This paper aims to examine the design and physics of a spectrophotometer, explain atomic spectroscopic concepts, collect and analyse primary and secondary data from a spectrophotometer for hydrogen and helium light sources, and discuss why spectrophotometers are useful to astronomers. The aforementioned is addressed through a series of research questions to guide the investigation.
How does each component within the spectrophotometer physically work and how does it contribute to the collection of accurate data on the spectral patterns of a light source?
A spectrophotometer is an instrument that is used to determine the angles at which light is diffracting by a grating, which can be substituted into the equation nλ = d*sin(θ) to determine the wavelength of the light. Figure 1 shows a diagram of the components of a spectrophotometer.
Light (electromagnetic radiation or EMR) from a light source enters an aperture referred to in Figure 1 as the collimating slit where it diffracts (as it is a wave). The distance between the collimating slit and the collimating lens is equal to the focal length of the lens, thus causing the diffracted light to travel through the lens which is a denser medium. When light travels through a denser medium, it will bend towards the normal. Consequently, the diffracted light beams are bent such that the light waves travel parallel to each other, which forms a narrow beam of light.
This beam of light strikes the diffraction grating which disperses the light into a spectrum. The diffraction grating is multiple slits positioned very closely together which causes the incident light to interfere upon travelling through the grating. The light waves form patterns of destructive and constructive interference. At points of constructive interference, the light intensity is especially high. The aforementioned equation – nλ = d*sin(θ) – demonstrates the angle at which a particular wavelength will constructively interfere, causing a point of high light intensity. d refers to the distance between the slits in the diffraction grating, θ is the angle of diffraction of the light after passing through the grating, λ is the wavelength of the light and n is the order of path difference (λ) as light will also constructively interfere at path difference equal to a wholenumber sum of wavelengths. Given that in a spectrophotometer d does not change, an increase in the angle (θ) will see an increase in the wavelength. As light colour is characterised by wavelength, different colours of light will be produced at different angles. The light then travels through a focusing lens whereby the parallel beam of colour passes through a slit on the aperture disk before the beam hits the high sensitivity light sensor. The readings gathered by the high sensitivity light sensor correspond with the angle, thus used to determine the wavelengths which are absorbed and emitted by the element using the nλ = d*sin(θ) formula.
What factors cause the emission and absorption spectral lines to vary between different elements and how can these factors be used to determine ideal conditions for accurate experimental results?
Niels Bohr developed the current theory for the model of an atom called the Bohr model (succeeding the Rutherford’s model) in 1913 (Figure 2). The Bohr model incorporates the absorption and emission spectra theory which is the basis of this paper. Bohr hypothesised that electrons exist in mutable states of radial orbit around the atom’s nucleus. However, he theorised that only specific orbital ranges were possible such that electrons could only orbit at specific distances away from the nuclei. A set level of energy is associated with electrons at the specific orbital ranges (Nave, 2002).
In Figure 2, the orbital level whereby n = 1 is the level with the lowest amount of energy, smallest radius, and closest to the nuclei. n = 1 is referred to as the ‘ground state’ of the electron. An increase in n increases the radius of the orbit and thus the electrons in that orbital level’s energy. An electron above the ground state is referred to as in an ‘excited state’ (Williams, 2016).
Louis de Broglie, a French physicist from Bohr’s era, hypothesised that the quantised orbital levels prove that electrons move as a circular standingwave which have a number of phases equal to the n value. Therefore, de Broglie theorised that the wave nature of electrons suggests that all matter has wave properties. Figure 3 envisages de Broglie’s theory.
The wavelength, integer and radius (r) of the electrons orbit with regard to the nucleus can be given by 2πr = nλ.
Julius Mayer in 1842, with the help of Antoine Lavoisier’s discovery of the law of conservation of mass in 1785, founded the law of conservation of energy. Mayer’s scientific law means that when an electron absorbs energy, it expends and transfers the energy in some form. Niels Bohr’s theory entails singleelectron atoms absorbing energy, whereby the electron jumps to a higher orbital or energy level when the energy is at a specific level. The electron then releases this energy in the form of light when it drops back down to its ground state (or a lower energy level). The energy of the light (photons) released equals the change in energy level across the levels in which it drops due to the conservation of energy. The formula ΔE = hf where E = energy, h = planks constant (6.62 x 10^{34} m^{2}kg/s) and f = frequency of the EMR (thus hf is the energy of the photon released) is used to express the energy emissions from the electrons.
The same formula is used in determining energy absorbed. This proves that only certain frequencies of light and thus wavelengths (due to formula f = v/λ) have the ability to absorb light because only specific energy levels (reflected by values of E) exist within a singleelectron atom. Thus, due to the proportionality of E to f in the formula ΔE = hf, specific values of E only allow for specific values of f to exist, given h is a constant. These specific values of f are frequencies, and thus calculate to be wavelengths as v in the formula f = v/λ is a universal constant (speed of light, 3 x 10^{8}), are the wavelengths that are absorbed and emitted. An increase in E causes an increase in f and thus and decrease in λ. This proportionality is displayed in Figure 4.
John Rydberg was a Swedish physicist who found a mathematical relationship between spectral lines in singleelectron atoms. He ultimately discovered there was an integer relationship between the wavenumbers of successive lines (Helmenstine, 2018). From this, he devised the formula 1/λ = R(1/n_{1}^{2} – 1/n_{2}^{2}) which is referred to as Rydberg’s equation. R is equal to 1.097 x 10^{7}m^{—1} (Rydberg’s constant).
Different elements comprise of discrete nuclear charge given the number of protons in the nucleus varies between elements. The nuclear charge dictates the energy levels by which an electron can move within. Therefore, different elements have different energy/orbital levels at the specific integers (n=1 to n=∞). These differing energy levels are what characterises an individual element’s unique spectrum, thus the element’s specific wavelengths of light emitted.
An absorption spectrum is made up of a continuous spectrum (see Figure 5) with lines of colour missing. The lines of colours missing in the absorption spectrum correspond with the lines that are present in the emission spectrum. Absorption refers to the process whereby an electron absorbs energy if it is exactly equal to one of the quantised energy levels the electron will jump up to that higher energy level (excited state) and conserve energy. However, electrons only stay at that energy level temporarily. When the electron returns to the ground state, it releases the same amount of energy it took to reach the excited state and emits the energy it conserved as a photon (light). Figure 5 shows a continuous spectrum and compares it with an absorption and emission spectrum to depict the correlation that exists between the two, such that dark lines in the absorption spectrum correlate with coloured lines in the emission spectrum (and the same relationship occurs contrariwise).
Each colour has a corresponding wavelength value, as shown in Figure 6. From the wavelength values, the change in energy in the electron can be determined and thus shows the energy levels of an element. This means that through analysing the spectrum of an unknown element, the element can be determined.
Précised, the dark lines on an absorption spectrum is a visual representation of the energies and wavelengths which an electron absorbs, hence causing the electron to jump to a higher energy level. Then, as the electron returns to its original energy level it emits photons at certain frequencies (and thus inversely proportional wavelengths) that are depicted on the emission spectrum. As different elements have different nuclear charges, they possess different energy levels, causing spectral lines to vary between elements.
Understanding the fundamentals of optical spectroscopy, particularly the aforementioned on spectral lines, energy levels, and other quantum theories assist in the understanding of a spectrophotometer’s purpose. Therefore, it can be determined that for accurate results, the only light that can be emitted into the collimating slit is the designated element’s light emitted by the light source. If other elements are producing light, the spectrophotometer may produce spectral lines from that source that occur at wavelengths that the designated source would not have absorbed/emitted at, thus giving inaccurate results. The spectrophotometer used for primary data in this paper was covered to the greatest feasible extent such that the designated light source was the only source giving off light.
How can the particular properties of stars be determined through optical spectroscopy and in what way has this instigated advancement in the area of astronomy?
Many properties of stars can be revealed spectroscopy techniques such as the stars temperature, luminosity, chemical composition, age, and relative motion (using Doppler effect calculations). Additionally, spectroscopy is used to identify physical properties of plants, nebulae, active galactic nuclei, galaxies, and other celestial matter.
Temperature. Gustav Kirchhoff, a German physicist, proposed in 1860 the idea of a blackbody. A blackbody is a material that emits EMR at all wavelengths. Stars are said to behave very similarly to blackbodies which explains why stars change colours over the course of their lifetimes. In 1894 Wilhelm Wien formatted an expression linking the temperature (T) of a blackbody to its peak emission wavelength (λ_{max}) being b = λ_{max}T where b is a constant of proportionality equal to 2.898 x 10^{3} (Wien’s displacement constant). The equation is referred to as Wien’s Law. The surface temperature of a star can be determined by measure its peak wavelength. Figure 7 shows the relationship between peak wavelength and spectral radiance (intensity), with the plotted values on the graph (i.e. 5000K) referring to the temperature at the given wavelength in a blackbody such that at 5000K (kelvins) is equal to 613nm (nanometres). Given a blackbody only approximates the circumstances of a star, the data should not be determined as completely accurate but rather plausible estimations.
Luminosity. The luminosity of a star refers to its intrinsic brightness, mathematically given as the rate of EMR emission. Luminosity (L) can be linked to temperature of a star through the expression L = 4πR^{2}σT^{4}, where R refers to the radius of the star and σ is equal to 5.67 x 10^{8} Wm^{2}K^{4} (the StefanBoltzmann constant).
Chemical properties and composition. Astronomers can compare the absorption lines of a star to the emission spectra of known gases. This can help astronomers determine what gasses the star is composed of given they will correlate with the emissions of gasses tested using a spectrophotometer. The significant Fraunhofer lines (dark lines produced in the absorption spectrum) are depicted in Figure 8.
If a star is emitting wavelengths of these particular values, it can be determined that the star is at least somewhat composed of the element corresponding to that wavelength.
Age. The approximate age of a star can be determined through analysis of the stars chemical composition, calculated through analysis of spectrum of the star vs. spectrum of known gasses. Stars are comprised of hydrogen and helium early in their lives. When the star reaches a temperature (which can be determined using aforementioned equations) of approximately 14.5 x 10^{6} kelvins as it ages, nuclear fusion starts to occur. Heavier elements are synthesised and helium atoms fuse together until iron is produced. As stars do not have the ability to create heavier elements past iron given they would collapse on themselves as a result of increased gravity and density, a supernova generally occurs next which fuses iron into heavier elements and then spreads across the galaxy, causing a new series of stars to be formed. Hence, stars with a lower amount of helium and hydrogen are estimated to be younger than stars with high amounts of those two elements.
Relative motion. To understand star motion relative to Earth, it must first be known that stars and interstellar gasses are bound by gravity to form galaxies, such as the Milky Way. Groups of galaxies can be bound by gravity in galaxy clusters as well. Hence, with the exception of some stars in local galaxies and in the Milky Way, almost all galaxies containing stars are moving away from Earth due to the expansion of the universe. The velocity of a star with respect to an observer is referred to as radial velocity. As mentioned before, spectral emission lines display specific wavelengths which can be determined as frequencies given the formula v=λf (v is sometimes depicted as c – universal constant speed of light NOT the velocity of a specific star). Using spectroscopy techniques to evaluate the wavelengths radiating off a star the frequencies can then be measured using the Doppler effect rules. The Doppler effect states that objects moving towards the observer have larger frequencies (thus smaller wavelengths due to the inverse proportionality between λ and f) and objects moving away from an observer have smaller frequencies (larger wavelengths). Referring to Figure 6, it can be seen that smaller wavelengths on the visible spectrum tend to have an indigoblue colour whilst larger wavelengths have a red colour. Therefore, it is said that objects moving towards us are blueshifted and objects moving away are redshifted, meaning that stars moving towards us appear bluer than they actually are and stars moving away appear redder. The Doppler effect expression
is:
where λ_{0} is the emitted wavelength of the star, v_{0} is the velocity of the star and λ is the observed wavelength. When v<0, λ< λ_{0} and thus a blueshifted wavelength is observed. Redshift (z) can be expressed by the following equations (Figure 9):
In 1913, Vesto Silpher determined that the Andromeda Galaxy was blueshifted, meaning it was moving towards the Milky Way. Edwin Hubble went on to use Slipher’s research to define Hubble’s Law which is generalised to: v = H_{0} d whereby v is velocity or Hubble flow (cause of galaxies to recede from each other, describing the motion of galaxies solely due to the expansion of the Universe), H_{0} is the Hubble Constant (500km/s/Mpc, although theoretically continually increasing), and d is the distance from Earth. The Doppler effect and Hubble’s Law can be combined to form the expression z = v_{Hubble}/c where c is the speed of light. Précised, if the observed wavelength is greater than the actual wavelength emitted by a star, the star will appear red, as red has a greater wavelength, and the Doppler effect formula tells us that this means the star must be moving away from Earth as this mathematically makes v/c a positive number, and given c is a positive constant, v must be positive as well, thus positive velocity implying motion receding from us, the observers (Howell, 2014). Figure
10 demonstrates this visually on a continuous spectrum.
If the difference between the observed wavelengths and the actual wavelengths were equal to zero, the velocity would equal zero, and thus the rate of motion between earth and the star would be exactly the same. Figure 10 demonstrates how the Doppler effect and the motion of stars correspond with studies on optical spectroscopy.
With regard to the aforementioned relationships between spectroscopy and astronomy, it is clear that spectroscopic techniques and notions have been imperative to the advancements in astronomy. Further astronomical study on stars would likely not be possible without the likes of Hubble, Kirchhoff, Wien, Rydberg, de Broglie, Bohr and other’s work in the study of spectroscopy on quantum and astrometric scales.
Why do primary experimental results differ from theoretical and secondary experimental results when studying optical spectroscopy, specifically when determining results using a spectrophotometer?
As mentioned, a spectrophotometer is used to ultimately determine the wavelengths of emission for certain elements. However, data is often initially provided by the instrument in the form of light intensity vs. rotational angle. Applying the formula nλ = d*sin(θ), the wavelength (at a specific integer) can ultimately be determined to establish the emission spectra of the light source. Using a spectrophotometer, primary data was gathered and then plotted on a light intensity vs. rotational angle graph. The primary data graphs (Figure 11 & 12) are as follows:
The symmetrical nature of the graphs in Figure 11 and Figure 12 are due to constructive interference patterns occurring either side of the central maxima (central antinode) which is also the 0^{th} order constructive interference fringe. The integers first order, second order, and so forth have interference patters that occur at equal distances from the central maxima thus are at equal angles difference from the central maximum, thus appearing symmetrical. Figure 13 displays this.
At ‘max’ points labelled on Figure 13, the angles between a max point of the same integer with respect to the central maximum are theoretically equal.
Knowing that the angle differences between n^{th} integers should be equal to each other, to determine the theta (θ) value, it must be known that theta is a measurement of the angle from the normal (see Figure 14). Thus, the theta value is the mean of the difference between two angles of the same integer value.
The following tables (Figure 15 & 16) have therefore been formed using values from the data in Figure 11 and Figure 12 and the nλ = d*sin(θ) formula:
Note – Data returned from the spectrophotometer presents angles with negative values. Therefore, the absolute value of the angles is taken when determining wavelength. CM = central maxima. d = 1.666 * 10^{6} as per spectrophotometer manual.
FIGURE 15 – HYDROGEN SPECTRUM
Peak 
Angle > CM 
CM > Angle 
Angle (θ) 
Wavelength (nm) 
1 
87 
55 
16 
459.2 
2 
93 
48.7 
22.15 
628.1^{} 
3 
121.7 
21.8 
49.95 
1275.3 
FIGURE 16 – HELIUM SPECTRUM
Peak 
Angle > CM 
CM > Angle 
Angle (θ) 
Wavelength (m) 
1 
71.4 
32.1 
19.65 
560.2 
2 
74.2 
29 
22.6 
640.2 
3 
75.5 
27.4 
24.05 
679 
4 
90.6 
12.3 
26.1 
732.9 
Below is secondary data on the emission spectrum of these two elements:



Wavelengths (nm) of emission 



Hydrogen 
418.1 
439.3 
487.6 
655.0 


Helium 
388.8 
501.4 
587.4 
667.5 
706.2 

Wavelengths recorded in the secondary data are as follows in Figure 19.
The secondary data was gathered from a Northern Illinois University investigation authored by Richard Born in March 2014.
In determining theoretical results for the gasses, the Rydberg Series and other series can be used: λ_{vacuum}^{1} = RZ^{2}(1/n_{1}^{2} – 1/n_{2}^{2}), where: λ_{vacuum}^{1} is the wavenumber, an inverse of the wavelength in a theoretical vacuum, R is Rydberg’s Constant 1.0974 x 10^{7}/m, Z is the number of protons in the atomic nucleus of a hydrogenlike element (singleelectron elements), or the atomic number, and n are integers such that n_{1} is less than n_{2} which correspond to principle quantum numbers of the orbitals involved before and after the electron jumps to that shell. Helium is a hydrogenlike atom.
In determining the wavelengths of emission of hydrogen, all variables besides λ_{vacuum} must be known. As hydrogen has one proton in its nucleus, the Z number value is equal to 1, and for helium is 2. The n (integer) value is determined by what levels the electrons are jumping between. In gauging emissions, n_{1} will always equal 1 as this is the ground state integer. Given there are no positive integers less than one, the n_{2} value must be equal to or greater than one (whole numbers) as n_{1}<n_{2}.
Rydberg’s equation is generally used whereby n_{1} equals 1, 2 or 3. The Lyman Series refers to where n_{1} equals 1 and n_{2} equals between 2 and 6, the Balmer Series where n_{1} equals 2 and n_{2} equals between 3 and 6 and the Paschen Series where n_{1} equals 3 and n_{2} equals between 4 and 6. Figure 20 shows a table where Rydberg’s equation is used to determine the wavelength emissions for hydrogen at specified n values in the aforementioned series’, and Figure 21 for helium.
n_{1} 
n_{2}_{} 
Equation 
Emitted wavelength (nm) 
1 
2 
(1.0974*10^{7}*1^{2}(1/1^{2} – 1/2^{2}))^{1} 
121.49 
1 
3 
(1.0974*10^{7}*1^{2}(1/1^{2} – 1/3^{2}))^{1} 
102.52 
1 
4 
(1.0974*10^{7}*1^{2}(1/1^{2} – 1/4^{2}))^{1} 
97.2 
1 
5 
(1.0974*10^{7}*1^{2}(1/1^{2} – 1/5^{2}))^{1} 
94.92 
1 
6 
(1.0974*10^{7}*1^{2}(1/1^{2} – 1/6^{2}))^{1} 
93.73 
2 
3 
(1.0974*10^{7}*1^{2}(1/2^{2} – 1/3^{2}))^{1} 
656.1 
2 
4 
(1.0974*10^{7}*1^{2}(1/2^{2} – 1/4^{2}))^{1} 
486 
2 
5 
(1.0974*10^{7}*1^{2}(1/2^{2} – 1/5^{2}))^{1} 
433.93 
2 
6 
(1.0974*10^{7}*1^{2}(1/2^{2} – 1/6^{2}))^{1} 
410.06 
3 
4 
(1.0974*10^{7}*1^{2}(1/3^{2} – 1/4^{2}))^{1} 
1874.56 
3 
5 
(1.0974*10^{7}*1^{2}(1/3^{2} – 1/5^{2}))^{1} 
1281.44 
3 
6 
(1.0974*10^{7}*1^{2}(1/3^{2} – 1/6^{2}))^{1} 
1093.5 
n_{1}_{} 
n_{2}_{} 
Equation 
Emitted wavelength (nm) 
1 
2 
(1.0974*10^{7}*2^{2}(1/1^{2} – 1/2^{2}))^{1} 
30.37 
1 
3 
(1.0974*10^{7}*2^{2}(1/1^{2} – 1/3^{2}))^{1} 
25.63 
1 
4 
(1.0974*10^{7}*2^{2}(1/1^{2} – 1/4^{2}))^{1} 
24.3 
1 
5 
(1.0974*10^{7}*2^{2}(1/1^{2} – 1/5^{2}))^{1} 
23.73 
1 
6 
(1.0974*10^{7}*2^{2}(1/1^{2} – 1/6^{2}))^{1} 
23.43 
2 
3 
(1.0974*10^{7}*2^{2}(1/2^{2} – 1/3^{2}))^{1} 
164.02 
2 
4 
(1.0974*10^{7}*2^{2}(1/2^{2} – 1/4^{2}))^{1} 
121.5 
2 
5 
(1.0974*10^{7}*2^{2}(1/2^{2} – 1/5^{2}))^{1} 
108.48 
2 
6 
(1.0974*10^{7}*2^{2}(1/2^{2} – 1/6^{2}))^{1} 
102.52 
3 
4 
(1.0974*10^{7}*2^{2}(1/3^{2} – 1/4^{2}))^{1} 
468.64 
3 
5 
(1.0974*10^{7}*2^{2}(1/3^{2} – 1/5^{2}))^{1} 
320.36 
3 
6 
(1.0974*10^{7}*2^{2}(1/3^{2} – 1/6^{2}))^{1} 
273.37 
Lyman Series Balmer Series Paschen Series
A relationship between hydrogen and helium wavelength emissions can be observed here. Due to the Z value variances between Rydberg’s formula for the two gasses, the emitted wavelength for helium at the corresponding n_{1} and n_{2} values is the wavelength for hydrogen divided by 4 (λ_{hydrogen}/4 = λ_{helium}).
Figure 22 and 23 combine the primary, secondary and theoretical wavelengths for hydrogen and helium on/near the visible colour spectrum to demonstrate comparisons.
Primary wavelengths (nm) 
Secondary wavelengths (nm) 
Theoretical wavelengths (nm) 

418.1 
410.1 
459.2 
439.3 
433.9 

487.6 
486 
628.1 
655.0 
656.1 
Primary wavelengths (nm) 
Secondary wavelengths (nm) 
Theoretical wavelengths (nm) 


273.4 


320.4 

388.8 



468.6 

501.4 

560.2 
587.4 

640.2 


679 
667.5 

732.9 
706.2 

Figure 24 and 25 visualises this through showing these wavelengths on a spectrum compared against each other.
Firstly, an explanation for differences in theoretical data vs. practical data (primary and secondary) may be that theoretical data measures wavelengths in a vacuum. The practical experiments using spectrophotometers were conducted in air, which effects wavelength. Theoretically, wavelengths in a vacuum can be converted to air using Donald Morton’s formula λ_{air} = λ_{vac}/n where n = 1 + 0.0000834254 + 0.02406147 / (130  s^{2}) + 0.00015998 / (38.9  s^{2}) and where s = 10^{4} / λ_{vac}, although Morton’s conversion theory is not yet widely accepted by experts in the field of physics. However, variances between theoretical and practical data on the helium spectrum are too great to attribute to small discrepancies with regard to the medium in which the EMR travels, particularly when comparing a vacuum to Earth’s atmosphere.
Although it is said that Rydberg’s formula should work for all hydrogenlike elements, the relationship whereby when Z > 1 wavelength can be given by λ_{hydrogen}/Z^{2}, thus prohibiting wavelength from being greater than that of hydrogens at any corresponding n_{1} and n_{2} values suggests that Rydberg’s formula is inapplicable to helium, at least when using the aforementioned three series for n values.
Concerning primary data, an assumption was made that the angles (which returned as negative) were positive and thus the absolute value was taken of them. This assumption may be incorrect, although it was the most practical interpretation that could be made. With regard to hydrogen, the secondary and theoretical data spectrums reflect each other relatively accurately, with a maximum variance between the two data sets of 8nm. This is the only pair of consistent data between the three data forms across the two elements.
To establish disparities (rather than anomalies in the data as all primary data appears to be incorrect), assumptions on the patterns of outcome wavelengths in comparison to secondary data must be made. It is possible that the emitted wavelengths (in hydrogen primary data) of 459.2nm and 628.1nm correspond with the 487.6nm and 655nm emitted in the secondary data. When the matching secondary and primary wavelengths are subtracted, differences of 28.4 nm and 26.9 nm respectively can be observed. These differences are very close in value, which suggests something in the spectrophotometer may have been causing discrepancies in the data.
Some possible issues with the spectrophotometer can be suggested, although there is no certainty as to what caused incongruent data. This could be an error in the placement of the lenses such that the slits are not at the focal point of the lens which would cause the rays to not be parallel when they strike the diffraction grating, causing incorrect results. Another issue may involve the spectrophotometers focusing lens being positioned such that the light intensity sensor is not placed at the focal point of the focusing lens. This would also reason inaccurate results. Furthermore, the d value sourced from the spectrophotometers manual could be incorrect and cause the postexperiment calculations to be incorrect. Any slight damages to the internal equipment in the spectrophotometer could alter results such that they are incorrect. These damages could be a result of the equipment wearing over time.
Primary data for helium possible appears to be shifted positively with respect to secondary data, however some data is missing, similar to hydrogen. Missing data could be attributed to any of the aforementioned possible causes for inaccuracies. The light sensor’s ability to gauge light intensity may not be adequate, although, again, there is no evidence to back this postulation.
Conclusion
The area of optical spectroscopy provides astrophysicists and general physicists with a wealth of data which can be used to examine wave and electron behaviour on quantum and universal levels. The primary research included in this paper whereby a spectrophotometer was used did not provide accurate results. Furthermore, whilst theoretical calculations returned correct results when studying hydrogen, theoretical calculations for helium did not show results that were reflected by secondary data and research. Regardless, the spectrophotometer is (and has been) an exceedingly useful mechanism for physicists when it returns accurate results. The emission and absorption spectrums historically determined spectroscopically are fundamental aspects of the physical nature of the universe, thus proving the study of optical spectroscopy as highly significant and vital to our understanding of physics nowadays.
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Appendix
 Glossary of terms
Photon
A particle representing a quantum of light or other form of electromagnetic radiation that has zero rest mass but carries energy proportional to the radiation frequency.
Element
A substance that cannot be chemically interconverted or dissected into simpler substances as it is a primary constituent of matter characterised by a specific quantity of protons that the atom has.
Focal length
The distance between the centre of a lens and a point where it is focused at infinity.
Integer
A whole number which is not a fraction (i.e. 8, 13, 592 not 8.4, 13.59, 592.01).
Diffraction
Where a beam of light (or other wave) spreads out as a result of passing through an aperture or across an edge.
Wavelength
The distance between successive points in a wave.
Frequency
The number of wave phases that are completed within a second.
EMR
Electromagnetic Radiation; a type of radiation whereby electric and magnetic fields varies simultaneously.
Interstellar
Situated between stars in the Universe.
Spectroscopy
The area of physics regarding investigation of the spectra produced when matter interacts with or emits electromagnetic radiation.
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