We can see the blue light coming from a germicidal UV lamp with our unaided eyes. Its main wavelength was 253.7 nm. However, it stands to reason that humans cannot see UV light with the naked eye. As a result, I will investigate several sources of blue light from the UV germicidal lamp, such as blue light from the UV lamp, scattered light, etc. This investigation will highlight the UV germicidal lamp as the main source of blue light. We will also investigate the physical conditions that cause UV light to emit visible blue light. We will then suggest on how to search for a tiny particle that is present near atoms whose mass ( eV) is less than that of the electrons.

1. UV Light Emitting Mechanism of a Germicidal UV Lamp

Figure 1 shows a schematic representation of the mercury (Hg) gas-filled germicidal lamp's UV light emitting mechanism. The four mechanisms by a germicidal lamp emits UV light through four processes, heating filament, thermal-emitting electron, electron scattering with Hg atoms, and UV emission.

Figure 1. (Color online) A schematic view of UV light emitting mechanism.

A UV lamp's filament is heated in the first process. In the second method, a hot filament emits a thermal electron. The thermal electron strikes a mercury atom in the third process, causing it to be become excited. Finally, a UV light is emitted in the fourth process when the excited mercury atom is de-excited. Fundamentally, when an excited electron is de-excited, rather than when a nucleus is stimulated, the excited electron releases UV light. These four processes describe a mechanism by which a germicidal UV lamp emits UV radiation. The interaction between a thermal electron and a mercury atom in a lamp is shown in Eq. (1) as the source of UV light. The symbols e_th, e, Hg, and Hg* indicate a thermal electron, a de-excited electron, a mercury atom, and an exciting mercury atom, respectively.

Through the transparency quarts tube of the lamp, the UV light is released. If the wall of the quart tube is coated with a fluorescent material, the UV light hits the fluorescent material, which causes the fluorescent light to be emitted. It is known as a fluorescent lamp.

1. Wavelength Distribution of UV Light of Germicidal Lamp

When an electron hits a metal surface, either an X-ray or UV light is produce. We can determine the UV light's wavelength by emitted a simple calculation on an excited mercury atom. Early in the 20th century, Moseley calculated the relationship between X-ray wavelength and atomic number. Equation (1)[1] can be used to calculate the wavelength of the wave caused by electron hitting a metal.

R is a Rydberg constant (1.097373⋅107/m) when the mass of the nucleus is infinite, while the Rydberg energy is 13.61 eV[2]. And, s = 1 for K-shell, 2 for L-shell, 3 for M-shell, respectively, and s<n.

We call the UV light, whose wavelength is longer than 100 nm and shorter than 380 nm, corresponding to the higher energy of 5.23 eV and lower than 19.9 eV. The interaction between an electron and a mercury atom in a germicidal lamp produces many types of UV. The wavelengths of UV light from the mercury germicidal lamp are fixed, but the intensity of UV light varies with the conditions. Figure 2 shows the efficiency of the mercury lamp depending on the vapor pressure of the mercury lamp. Figure 2 was redrawn from a graph described in a chemical data book[3]. Therefore, we can categorize the pressure of the mercury lamps into 3 regions. In region 1 (R1), especially at pressure of 0.01 mmHg, a UV light with wavelength λ= 253.7 nm dominates for a UV light and λ= 435.8 nm for a visible light range. While, in region 2 (R2), for the pressure near 760 mmHg, a UV light with wavelength λ= 365.0 nm dominates for a UV light and λ=5570–579.1 nm for a visible light range.

Figure 2. (Color online) Efficiency of Hg lamp.

The distribution of UV light from a mercury lamp depends on the lamp's manufacture. Figure 3 shows the energy distribution of UV light made by a manufacturer. This graph was redrawn using the data provided by the manufacturer.

Figure 3. (Color online) Relative energy distribution of Hg lamp.

From the graph in Fig. 3, we see that a UV light with wavelength λ= 253.7 nm dominates in the UV range while a blue light λ= 435.8 nm and a purple light λ≈400 nm dominate in the visible range. As we see, the relative energy of visible light, blue and purple, from a germicidal lamp is less than 3%, while the relative energy contribution of UV light is close to 87%. Also, we can see another UV light λ≈ 364.0 nm, whose relative energy contribution is 1.5%.

In this study, I focused on the four UV lights whose wavelengths are less than 380 nm and whether they affect the amount of blue light and visible light. The wavelength of light, a type of electromagnetic wave, can be shifted for several reasons. For example, Raman scattering, Compton scattering, the Doppler's effect, etc. However, this investigation did not consider Doppler's effect because the UV source and detector do not move. Also, I did not consider that fluorescent light was produced by the interaction between UV light and fluorescent material surrounding the UV lamp.

1. For Compton scattering

We can calculate the shifted wavelength by the Compton scattering between a UV light and the electron of a mercury atom as

where λ and λ′ are the wavelengths of UV light before and after Compton scattering. Theoretically, the maximum wavelength difference (=0.24 nm) occurs with θ=π. The changed wavelength, Δλ, is ten thousand times smaller than that of UV light, λ sub 100 nm.

2. For Raman scattering

We can calculate the shifted wavelength from the Raman scattering between a UV light and the electron of a mercury atom as

where ν and ν′ are the frequency of UV light before and after Raman scattering. The maximum wavelength shift from Raman scattering could be up to Δλ 106 nm. This maximum wavelength shift is reasonable when we think of the vibration frequency of the Cesium atom, 9.2⋅109 Hz. We can get this value because all the Boltzmann energy turns into vibration energy.

where KB,T, and h are Boltzmann constant, the temperature in Kelvin, and the Plank constant.

This result gives us the information that a small amount of the shifted frequency by Raman scattering could shift the UV light to visible light.

We investigated several ways to produce blue and visible light in UV germicidal mercury lamps. The blue light should come from the lamp itself, majorly. But several physics effects could shift the wavelength, which then makes the wavelength of UV light shift into the visible light range. A Raman scattering, a Compton scattering, a Doppler's effect, etc., could be the physical effects that shift the wavelengths of incident UV light. In this study, I focused on whether Raman scattering and Compton scattering can modify the wavelength of UV light from a germicidal lamp.

By the calculation, we know that a Raman scattering can shift the wavelength of the incident wave up to Δλ 106 nm in the ideal condition. So, small amount of wavelength shift by Raman scattering could make the UV light turn into the visible light range. In the following study, I will investigate how much UV light from a mercury germicidal lamp could turn into visible light.

Also, by the calculation, we know that a Compton scattering can shift the wavelength of the incident wave up to Δλ 0.24 nm. However, this wavelength shift is negligible compared with the UV light wavelength Δλ  ⋅102 nm, which is 10⁵ times larger than the wavelength shifted by Compton scattering.

We investigated whether the major reason UV light in a germicidal lamp shifted into the visible region is a Raman scattering rather than a Compton scattering when we consider only two scatterings.

We can consider another reason except for the Raman and Compton scattering described above. As we see, the effect of Compton scattering shifting is insignificant Δλ 0.24 nm. A Compton scattering shifts the wavelength as Δλ=λ′−λ=hmc(1−cosθ), where m is mass of the target. We calculate the wavelength shift by Compton scattering with m as the mass of the electron. If the mass target is much smaller than the mass of the electron, we can see the wavelength shift effect majorly. For example, if the target mass is 103−104 times smaller than the mass of the electron, the wavelength shifted by the Compton scattering reaches 2.4–24.0 nm. So, if there is a particle smaller than an electron in the atom, we could find a clue to the existence of a particle whose mass is lighter than that of the electron in or around an atom. For example, the particles whose mass is 1 eV can shift UV light around 2.0 nm by Compton scattering. Figure 4 shows the shifted wavelength of UV light due to a Compton scattering in the function of target particles. If there is a neutral particle near the atoms, we can achieve a clue using the procedure in this study. This tiny neutral particle could be a candidate for a dark matter that was introduced by V. Rubin in 1983[4]. Our research team has studied the search for non-baryonic dark matter, especially a WIMP with a mass of the sub-hundred GeV[5-9]. The study will be continued with a red shift of UV light from a germicidal lamp and tiny particles around the atoms. Figure 5 shows the expected wavelength shift of UV light due to Compton scattering. A red dashed line indicates the red-shifted UV light due to the Compton scattering. I expected that the peak would move to red while the width of the height broadened. I only mentioned a Compton scattering that makes a UV light shift in this investigation. In the following study, I will describe a Raman scattering that makes a UV light shift.

Figure 4. (Color online) Wavelengths of UV light shifted by Compton scattering.

Figure 5. (Color online) Expected wavelength shift due to Compton scattering.

This work was supported by the grant of NRF-2021R1F1A1061174.