The most prominent line in the spectrum of mercury is at 253.652 nm. Other lines are located at 365.01 nm, 404.65 nm, 435.83 nm, and 1013.97 nm. (4 points) (a) Which of these lines are located within the visible spectrum? What color are they? Which of these lines represents the most energetic light? What is the frequency of the most prominent line? Use the equation € = Av (c – speed of light; V = frequency, A – wavelength). Check the units before plugging in the numbers to the equation. Spectral Distribution of a Low-Pressure Mercury Lamp used wavelength calibration 10′ 0 10 ? L 10 ” 200 300 400 Wavelength (nm) 500 600
The most prominent line in the spectrum of mercury is at 253.652 nm. Other lines are located at 365.01 nm, 404.65 nm, 435.83 nm, and 1013.97 nm. (4 points) (a) Which of these lines are located within the visible spectrum? What color are they? Which of these lines represents the most energetic light? What is the frequency of the most prominent line? Use the equation € = Av (c – speed of light; V = frequency, A – wavelength). Check the units before plugging in the numbers to the equation. Spectral Distribution of a Low-Pressure Mercury Lamp used wavelength calibration 10′ 0 10 ? L 10 ” 200 300 400 Wavelength (nm) 500 6
The Correct Answer and Explanation is:
To answer the question thoroughly, let’s break it down into four parts:
Given Wavelengths:
- 253.652 nm (most prominent line)
- 365.01 nm
- 404.65 nm
- 435.83 nm
- 1013.97 nm
(a) Which lines are in the visible spectrum? What color are they?
The visible spectrum ranges approximately from 380 nm to 750 nm.
Within the visible range:
- 365.01 nm: Just outside visible range (near UV)
- 404.65 nm: Visible, violet
- 435.83 nm: Visible, blue
- 1013.97 nm: Infrared, not visible
- 253.652 nm: Ultraviolet, not visible
✅ Visible lines and colors:
- 404.65 nm → Violet
- 435.83 nm → Blue
(b) Which line represents the most energetic light?
The energy of a photon is inversely proportional to its wavelength: E=h⋅ν=h⋅cλE = h \cdot \nu = \frac{h \cdot c}{\lambda}
So, shorter wavelength = higher energy.
Among the given wavelengths, the shortest is 253.652 nm, meaning it is the most energetic light.
(c) What is the frequency of the most prominent line (253.652 nm)?
Use the equation: c=λ⋅ν⇒ν=cλc = \lambda \cdot \nu \Rightarrow \nu = \frac{c}{\lambda}
Where:
- c=3.00×108 m/sc = 3.00 \times 10^8 \, \text{m/s}
- λ=253.652 nm=253.652×10−9 m\lambda = 253.652 \, \text{nm} = 253.652 \times 10^{-9} \, \text{m}
ν=3.00×108253.652×10−9≈1.182×1015 Hz\nu = \frac{3.00 \times 10^8}{253.652 \times 10^{-9}} \approx 1.182 \times 10^{15} \, \text{Hz}
✅ Frequency of 253.652 nm line: 1.182×1015 Hz\boxed{1.182 \times 10^{15} \, \text{Hz}}
Explanation:
Mercury emits light at specific wavelengths due to electronic transitions between energy levels. These discrete spectral lines include ultraviolet (UV), visible, and infrared (IR) radiation. Among the provided wavelengths—253.652 nm, 365.01 nm, 404.65 nm, 435.83 nm, and 1013.97 nm—only 404.65 nm and 435.83 nm fall within the visible spectrum, which ranges from approximately 380 to 750 nm. The 404.65 nm line corresponds to violet, while the 435.83 nm line corresponds to blue. The 365.01 nm line lies just outside the visible range in the near-UV region. The 253.652 nm line, though the most prominent and intense emission of mercury, lies in the ultraviolet region, invisible to the human eye. The 1013.97 nm line lies in the infrared region.
The most energetic light corresponds to the shortest wavelength. According to the equation E=h⋅ν=h⋅cλE = h \cdot \nu = \frac{h \cdot c}{\lambda}, energy is inversely proportional to wavelength. Thus, the 253.652 nm line has the highest energy among those listed. To determine its frequency, we use ν=cλ\nu = \frac{c}{\lambda}, where cc is the speed of light (3.00 × 10⁸ m/s) and λ\lambda is converted to meters. Substituting, we find the frequency of the 253.652 nm line to be approximately 1.182 × 10¹⁵ Hz. This high frequency and energy make it ideal for applications like germicidal lamps and UV spectroscopy, despite being invisible to the naked eye.
