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Chapter 5: Problem 30

The following orbital-filling diagram represents an excited state rather than the ground state of an atom. Identify the atom, and give its ground-state electron configuration. $$ \text { [Ar] } \frac{\downarrow \uparrow}{4 s} \quad \underline{\downarrow \uparrow} \underline{\downarrow \uparrow} \frac{\downarrow \uparrow}{3 d} \stackrel{\downarrow \uparrow}{\downarrow \uparrow} \quad \frac{\downarrow \uparrow}{4 p}-\frac{\downarrow \uparrow}{4 p}- $$

Short Answer

Expert verified
The atom is Krypton (Kr), and its ground-state electron configuration is \([\text{Ar}]\, 3d^{10}\, 4s^{2}\, 4p^{6}\).

Step by step solution

01

Identify the Filled Orbitals in the Diagram

The given diagram shows the filled orbitals as follows:- Complete fill in the \(4s\) orbital: \(\uparrow\downarrow\)- Complete fill in the \(3d\) orbital: \(\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\) - Complete fill in the \(4p\) orbitals: \(\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\). This represents an excited electronic configuration.
02

Count the Total Number of Electrons

Count all the electrons from the filled orbitals:- \(4s\): 2 electrons- \(3d\): 10 electrons- \(4p\): 6 electronsThis sums up to a total of \(2 + 10 + 6 = 18\) electrons after the \([\text{Ar}]\) core, which already has 18 electrons. Therefore, the total atomic number is \(18 + 18 = 36\).
03

Identify the Element and Ground State

The atomic number 36 corresponds to the element Krypton (Kr). The ground state electron configuration for Krypton is \([\text{Ar}]\, 3d^{10}\, 4s^{2}\, 4p^{6}\), which is already represented correctly in its excited state form here.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Excited State
An excited state of an atom refers to a temporary energy level higher than the minimum possible energy. Atoms absorb energy, and electrons jump from their usual energy levels. This leap is outside their normal atomic shells. Here鈥檚 what you need to know about excited states:
  • The electrons do not follow the standard lowest energy filling order.
  • Energy absorption causes this, making electrons transfer to a higher orbital.
  • It's crucial to note that excited states aren't stable and tend to revert to the ground state, releasing energy in the process.
In our example, the orbital-filling diagram shows electrons in a non-conventional arrangement, indicating Krypton in an excited state. Unlike the ground state, electrons can be found in different orbitals than usual before releasing any absorbed energy.
Ground State
The ground state is the lowest energy state of an atom where electrons occupy the closest possible orbitals to the nucleus and follow known filling rules.Here are some essential points about the ground state:
  • Electrons fill orbitals from the lowest to highest energy levels typically.
  • It represents the most stable configuration of an atom.
  • For any atom, identifying its ground state provides insight into its chemical properties.
For Krypton, the ground state configuration is reached when all electrons are in their lowest possible energy levels: \[\text{Ground-state electron configuration: } [\text{Ar}]3d^{10}4s^24p^6\]It differs from the excited state as all electrons occupy the standard arrangement.
Orbital-Filling Diagram
An orbital-filling diagram illustrates the electron arrangement within an atom鈥檚 orbitals.
  • It uses arrows to represent electron spins within orbitals.
  • Each orbital can hold a maximum of two electrons with opposite spins.
  • The diagram visually shows the electron configuration of both ground and excited states.
Reading an orbital-filling diagram correctly is key to understanding whether an atom is in a ground or excited state. For the given problem, each filled orbital and its arrows provided clues that the atomic configuration didn鈥檛 conform to the typical pattern, indicating excitement. Understanding these diagrams helps with predicting and explaining chemical behaviors of an element.

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Most popular questions from this chapter

Calculate the wavelength and energy in kilojoules necessary to completely remove an electron from the second shell \((m=2)\) of a hydrogen atom \(\left(R_{\infty}=1.097 \times 10^{-2} \mathrm{~nm}^{-1}\right)\).

What is the wavelength in meters of photons with the following energies? In what region of the electromagnetic spectrum does each appear? (a) \(90.5 \mathrm{~kJ} / \mathrm{mol}\) (b) \(8.05 \times 10^{-4} \mathrm{~kJ} / \mathrm{mol}\) (c) \(1.83 \times 10^{3} \mathrm{~kJ} / \mathrm{mol}\)

The data encoded on CDs, DVDs, and Blu-ray discs is read by lasers. What is the wavelength in nanometers and the energy in joules of the following lasers? (a) CD laser, \(\nu=3.85 \times 10^{14} \mathrm{~s}^{-1}\) (b) DVD laser, \(\nu=4.62 \times 10^{14} \mathrm{~s}^{-1}\) (c) Blu-ray laser, \(\nu=7.41 \times 10^{14} \mathrm{~s}^{-1}\)

The MRI (magnetic resonance imaging) body scanners used in hospitals operate with \(400 \mathrm{MHz}\) radio frequency energy. How much energy does this correspond to in kilojoules per mole?

The biological effects of a given dose of electromagnetic energy generally become more serious as the energy of the radiation increases: Infrared radiation has a pleasant warming effect; ultraviolet radiation causes tanning and burning; and \(\mathrm{X}\) rays can cause considerable tissue damage. What energies in kilojoules per mole are associated with the following wavelengths: infrared radiation with \(\lambda=1.55 \times 10^{-6} \mathrm{~m}\), ultraviolet light with \(\lambda=250 \mathrm{~nm}\), and \(\mathrm{X}\) rays with \(\lambda=5.49 \mathrm{~nm} ?\)
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