The most prominent lines 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? (b) Which of these lines represents the most energetic light? (c) What is the frequency of the most prominent line? Use the equation c = lv (c – speed of light, v- frequency, 1 – wavelength). Check the units before plugging in the numbers to the equation. Spectral Distribution of a Low-Pressure Mercury Lamp used in wavelength calibration 10- 10 Relative Intensity 10- 10- 200 500 600 300 400 Wavelength (nm)
The Correct Answer and Explanation is :
Let’s address each part of your question regarding the mercury emission lines:
(a) Which of these lines are located within the visible spectrum? What color are they?
The visible spectrum for human eyes ranges from approximately 380 nm (violet) to 750 nm (red). citeturn0search16
- 253.652 nm: This wavelength falls in the ultraviolet (UV) range, which is below the visible spectrum.
- 365.01 nm: This wavelength is also in the UV range.
- 404.65 nm: This wavelength is in the violet range of the visible spectrum.
- 435.83 nm: This wavelength is in the blue range of the visible spectrum.
- 1013.97 nm: This wavelength is in the near-infrared (NIR) range, which is just beyond the visible spectrum.
(b) Which of these lines represents the most energetic light?
The energy of a photon is inversely proportional to its wavelength, as described by the equation:
E=h⋅cλE = \frac{h \cdot c}{\lambda}
Where:
- EE is energy
- hh is Planck’s constant (6.626×10−346.626 \times 10^{-34} J·s)
- cc is the speed of light (3.00×1083.00 \times 10^{8} m/s)
- λ\lambda is wavelength
Among the listed wavelengths, 253.652 nm is the shortest, corresponding to the highest energy.
(c) What is the frequency of the most prominent line?
The most prominent line is at 253.652 nm. To find its frequency (vv), we use the equation:
v=cλv = \frac{c}{\lambda}
Substituting the values:
v=3.00×108 m/s253.652×10−9 mv = \frac{3.00 \times 10^{8} \, \text{m/s}}{253.652 \times 10^{-9} \, \text{m}}
Calculating:
calculatorturn0calculator0
Therefore, the frequency of the most prominent mercury emission line is approximately 1.18 × 10¹⁴ Hz.
Summary:
- Visible Spectrum Lines: 404.65 nm (violet) and 435.83 nm (blue).
- Most Energetic Line: 253.652 nm (UV).
- Frequency of Most Prominent Line: Approximately 1.18 × 10¹⁴ Hz.
Understanding these properties is essential in fields like spectroscopy and photonics, where precise wavelength and frequency measurements are crucial for applications such as calibration, material analysis, and optical communication systems.