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Chapter 1: Problem 3

An electron from which peak would have the greatest velocity after ejection? (A) The peak at 104 \(\mathrm{MJ} / \mathrm{mol}\) (B) The peak at 6.84 \(\mathrm{MJ} / \mathrm{mol}\) (C) The peak at 4.98 \(\mathrm{MJ} / \mathrm{mol}\) (D) The peak at 1.76 \(\mathrm{MJ} / \mathrm{mol}\)

Short Answer

Expert verified
The electron from the peak at 104 MJ/mol would have the greatest velocity after ejection.

Step by step solution

01

Identify the Energy Level of Peaks

We identify the energy levels of the peaks from the options provided. They are: 104 MJ/mol, 6.84 MJ/mol, 4.98 MJ/mol and 1.76 MJ/mol.
02

Compare the Energy Levels

Next, compare the energy levels of the peaks. The peak with the highest energy level will result in the greatest velocity of the ejected electron.
03

Identify the Peak with Highest Energy Level

After comparing, we identify that the peak at 104 MJ/mol has the highest energy level among the options given.

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Key Concepts

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

Electron Velocity
In photoelectron spectroscopy, the velocity of ejected electrons is a crucial concept. Their velocity is determined by the energy transferred to the electron during the ejection process. When an electron absorbs energy, it gains kinetic energy, which translates into velocity. The relationship between kinetic energy and velocity is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass of the electron, and \( v \) is the velocity.
  • Higher energy absorption results in greater velocity.
  • The peak with the highest energy indicates the greatest acquired velocity.
In the given scenario, electrons released from the 104 MJ/mol peak achieve the highest velocity, as they receive the most energy.
Energy Levels
Energy levels play a pivotal role in determining the behavior of electrons in photoelectron spectroscopy. Each peak in the spectrum corresponds to a specific energy level, defining the amount of energy required to remove an electron from an atom.
The energy level is directly proportional to the energy needed to overcome the attractive forces holding the electron in its place:
  • A higher energy level means stronger attraction to the nucleus.
  • The peak at 104 MJ/mol indicates a high energy level, reflecting a strong cohesive force.
Thus, understanding energy levels helps predict which electrons will gain the most kinetic energy upon ejection.
Ejected Electrons
Ejected electrons are central to the analysis in photoelectron spectroscopy. They tell us about the internal energy structure of atoms. When these electrons are knocked out of an atom due to energy absorption, several factors influence their characteristics, such as velocity and direction.
Key factors of ejected electrons include:
  • Energy source: Determines the initial energy transferred to the electrons.
  • Kinetic energy: Relates to the velocity with which electrons leave the atom.
  • Detection: Helps in mapping out the energy distribution in the atom.
Studying the behavior of these ejected electrons gives insights into broader atomic properties and energy arrangements.

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Most popular questions from this chapter

Questions 54-56 refer to the following. GRAPH CAN'T COPY Between propane and ethene, which will likely have the higher boiling point and why? (A) Propane, because it has a greater molar mass (B) Propane, because it has a more polarizable electron cloud (C) Ethene, because of the double bond (D) Ethene, because it is smaller in size

Choose the correct net ionic equation representing the reaction that occurs when solutions of potassium carbonate and copper (I) chloride are mixed. (A) \(\mathrm{K}_{2} \mathrm{CO}_{3}(a q)+2 \mathrm{CuCl}(a q) \rightarrow 2 \mathrm{KCl}(a q)+\mathrm{Cu}_{2} \mathrm{CO}_{3}(s)\) (B) \(\mathrm{K}_{2} \mathrm{CO}_{3}(a q)+2 \mathrm{CuCl}(a q) \rightarrow 2 \mathrm{KCl}(\mathrm{s})+\mathrm{Cu}_{2} \mathrm{CO}_{3}(a q)\) (C) \(\mathrm{CO}_{3}^{2-}+2 \mathrm{Cu}^{+} \rightarrow \mathrm{Cu}_{2} \mathrm{CO}_{3}\) (D) \(\mathrm{CO}_{3}^{2-}+\mathrm{Cu}^{2+} \rightarrow \mathrm{CuCO}_{3}(s)\)

Directions: Questions 1-3 are long free-response questions that require about 23 minutes each to answer and are worth 10 points each. Write your response in the space provided following each question. Examples and equations may be included in your responses where appropriate. For calculations, clearly show the method used and the steps involved in arriving at your answers. You must show your work to receive credit for your answer. Pay attention to significant figures. A student is tasked with determining the identity of an unknown carbonate compound with a mass of 1.89 g. The compound is first placed in water, where it dissolves completely. The \(K_{s p}\) value for several carbonate-containing compounds are given below. $$\begin{array}{|c|c|}\hline \text { Compound } & {K_{s p}} \\ \hline \text { Lithium carbonate } & {8.15 \times 10^{-4}} \\ \hline \text { Nickel (II) carbonate } & {1.42 \times 10^{-7}} \\ \hline \text { Strontium carbonate } & {5.60 \times 10^{-10}} \\ \hline\end{array}$$ (a) In order to precipitate the maximum amount of the carbonate ions from solution, which of the following should be added to the carbonate solution: \(\operatorname{LiNO}_{3}, \mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2},\) or \(\mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2} ?\) Justify your answer. (b) For the carbonate compound that contains the cation chosen in part (a), determine the concentration of each ion of that compound in solution at equilibrium. (c) When mixing the solution, should the student ensure the carbonate solution or the nitrate solution is in excess? Justify your answer. (d) After titrating sufficient solution to precipitate out all of the carbonate ions, the student filters the solution before placing it in a crucible and heating it to drive off the water. After several heatings, the final mass of the precipitate remains constant and is determined to be 2.02 g. (i) Determine the number of moles of precipitate. (ii) Determine the mass of carbonate present in the precipitate. (e) Determine the percent, by mass, of carbonate in the original sample. (f) Is the original compound most likely lithium carbonate, sodium carbonate, or potassium carbonate? Justify your answer.

Use the following information to answer questions 25-28. A voltaic cell is created using the following half-cells: \(\begin{array}{ll}{\mathrm{Cr}^{3+}+3 e \rightarrow \mathrm{Cr}(s)} & {E^{\circ}=-0.41 \mathrm{V}} \\ {\mathrm{Pb}^{2+}+2 e \rightarrow \mathrm{Pb}(s)} & {E^{\circ}=-0.12 \mathrm{V}}\end{array}\) The concentrations of the solutions in each half-cell are 1.0 M. Which net ionic equation below represents a possible reaction that takes place when a strip of magnesium metal is oxidized by a solution of chromium (III) nitrate? (A) \(\operatorname{Mg}(s)+\operatorname{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cr}^{3+}(a q)+3 \mathrm{NO}_{3}^{-}(a q)\) (B) \(3 \mathrm{Mg}(s)+2 \mathrm{Cr}^{3+} \rightarrow 3 \mathrm{Mg}^{2+}+2 \mathrm{Cr}(s)\) (C) \(\mathrm{Mg}(s)+\mathrm{Cr}^{3+} \rightarrow \mathrm{Mg}^{2+}+\mathrm{Cr}(s)\) (D) \(3 \mathrm{Mg}(s)+2 \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q) \rightarrow 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{Cr}(s)+\mathrm{NO}_{3}^{-}(a q)\)

Even though it is a noble gas, xenon is known to form bonds with other elements. Which element from the options below would xenon most likely be able to bond with? (A) Lithium (B) Argon (C) Fluorine (D) Carbon
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