On a separate piece of paper answer each of the following questions. Be sure to use complete sentences where appropriate. For full credit be sure to show all of your work. 1. 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 = Avíc – speed of light, v – frequency, A-wavelength). Check the units 1 Spectral Distribution of a Low-Pressure Mercury Lamp used in wavelength calibration 10 100 before plugging in the numbers to the equation. 100 10- 200 500 600 300 400 Wavelength (nm) 2. Identify each of the following atoms/ions by their electron configurations (4 points): Trash Complete electron configuration Condensed electron configuration Atom/lon 2. Identify each of the following atoms/ions by their electron configurations (4 points): Complete electron configuration Condensed electron configuration Atom/lon 1s 2s 2p 3s 3p 452 3d10 4p3 a (a neutral particle) Ib. [Ar] (an ion with a negative two charge) 3. Using the periodic table, indicate which member of each pair is (3 points). Less metallic Mg or s Smaller atomic radii Kor Rb Lowest ionization energy Korp 4. Potassium is a highly reactive metal, while argon is an inert gas. Explain this difference based on their electron configurations (5 points). 5. Draw the orbital diagram for Zn2+ ( 4 points)
The Correct Answer and Explanation is :
Part 1
- Mercury Spectrum: (a) Visible Spectrum Lines and Their Colors:
The visible spectrum of light lies between 400 nm and 700 nm. From the given wavelengths, the lines within this range are:
- 365.01 nm – This falls in the ultraviolet range and is not visible.
- 404.65 nm – This is within the violet region.
- 435.83 nm – This is within the blue region. So, the visible lines are at 404.65 nm (violet) and 435.83 nm (blue). (b) Most Energetic Light:
The most energetic light corresponds to the shortest wavelength because energy and wavelength are inversely related (E = h * c / λ). The line at 253.652 nm represents the highest energy. (c) Frequency of the Most Prominent Line:
The frequency can be calculated using the equation:
[
c = \lambda \cdot \nu
]
Where: - ( c ) is the speed of light = ( 3.00 \times 10^8 \, \text{m/s} )
- ( \lambda ) is the wavelength in meters (253.652 nm = ( 253.652 \times 10^{-9} \, \text{m} )) Rearranging the equation for frequency:
[
\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8}{253.652 \times 10^{-9}} = 1.18 \times 10^{15} \, \text{Hz}
]
- Electron Configurations: (a) For the atom with the electron configuration ( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4p^3 ):
- Complete Electron Configuration: ( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^3 )
- Condensed Electron Configuration: [Ar] 3d^10 4s^2 4p^3 (This represents arsenic, As, a neutral particle.) (b) For the ion with the condensed electron configuration [Ar] ( 3d^10 4s^2 4p^6 ) and a negative two charge:
- Complete Electron Configuration: ( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 )
- Condensed Electron Configuration: [Ar] ( 3d^{10} 4s^2 4p^6 ) (This represents the Se(^{2-}) ion.)
- Comparing Elements:
- Less Metallic: Between Mg and Si, Si is less metallic as it is closer to the metalloid category.
- Smaller Atomic Radii: Between K and Rb, K has a smaller atomic radius because it is higher in the periodic table.
- Lowest Ionization Energy: Between K and Rb, Rb has a lower ionization energy as it is lower in the periodic table, where the atomic radius increases, making it easier to remove an electron.
- Potassium vs. Argon:
- Electron Configurations: Potassium (K) has an electron configuration of [Ar] 4s^1, while Argon (Ar) has [Ne] 3s^2 3p^6.
- Explanation: Potassium has one electron in its outermost shell, which it can easily lose, making it highly reactive. Argon, on the other hand, has a full outer shell and is chemically inert because it doesn’t need to gain or lose electrons.
- Orbital Diagram for Zn²⁺:
- Zinc (Zn) has the electron configuration [Ar] 3d^10 4s^2. For Zn²⁺, two electrons are removed, usually from the 4s orbital.
- The electron configuration for Zn²⁺ is [Ar] 3d^10.
- The orbital diagram would show:
[
\text{3d: ↑↓ ↑↓ ↑↓ ↑↓ ↑↓}
]
There are 10 electrons in the 3d orbital, all paired.
Explanation of Concepts:
- The wavelength and frequency relationship is fundamental in determining the energy of light. Shorter wavelengths (like 253.652 nm) correspond to higher energy and frequency, as per the equation ( E = h \cdot \nu ).
- Electron configurations describe the arrangement of electrons in an atom or ion, which influences their chemical properties and reactivity. Potassium’s single electron in its outer shell explains its high reactivity, whereas Argon’s full shell makes it inert.
- Orbital diagrams show how electrons are arranged in orbitals. The Zn²⁺ ion has a stable configuration with all 3d electrons paired, which makes it less reactive compared to neutral zinc.