Investigating Energy Levels
Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation
where RH is the same as for hydrogen (2.179 × 10−18 J). Answer the following questions, without calculating energy values.
- a How would the ground-state energy levels of X and H compare?
- b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer.
- c How do the spacings of the energy levels of X and H compare?
- d Which would involve the emission of a higher
frequency of light , the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? - e Which atom, X or H, would require more energy to completely remove its electron?
- f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.
(a)
Interpretation:
The energy of ground state of atom X and H has to be compared.
Concept introduction:
Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion. By using this he derived a formula for energy levels of electron in H-atom.
Explanation of Solution
To compare: The energy of ground state of atom X and H.
The energy of ground state of atom X and H are same because the n value of ground state is same.
The energy of ground state of atom X and H was compared.
(b)
Interpretation:
The energy of atom X in level two and H in level two has to be compared.
Concept introduction:
Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion. By using this he derived a formula for energy levels of electron in H-atom.
Answer to Problem 7.24QP
Energy of an electron in X atom is lower than H atom.
Explanation of Solution
To compare: The energy of atom X in level two and H in level two.
When n value of H atom is two then
By using the formula of energy levels, the energy of atom X in level two and H in level two was compared.
(c)
Interpretation:
The energy level spacing of atom X and H has to be compared.
Concept introduction:
Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion. By using this he derived a formula for energy levels of electron in H-atom.
Explanation of Solution
To compare: The energy level spacing of atom X and H.
The energy level spacing of hydrogen is greater than X because the
The ratio of energy of H atom and X atom is
The energy level spacing of atom X and H was compared using the formula for energy levels.
(d)
Interpretation:
The atom which emits higher frequency of light when transition occurs has to be identified.
Concept introduction:
Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion. By using this he derived a formula for energy levels of electron in H-atom.
Answer to Problem 7.24QP
Hydrogen emits more frequency of light when transition occurs.
Explanation of Solution
To identify: The atom which emits higher frequency of light when transition occurs.
Energy and frequency are directly proportional to each other. Moreover the energy level spacing of hydrogen is greater than X atom. Thus, hydrogen emits more frequency of light when transition occurs.
The atom which emits higher frequency of light when transition occurs was identified.
(e)
Interpretation:
The atom which needs more energy to remove electron has to be identified.
Concept introduction:
Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion. By using this he derived a formula for energy levels of electron in H-atom.
Explanation of Solution
To identify: The atom which needs more energy to remove electron.
When the electrons in both atom present in ground state, then same amount of energy is utilized to remove electron. But, it requires different energies when electron is in different state.
The atom which needs more energy to remove an electron was identified.
(f)
Interpretation:
The frequency of light used for transition from
Concept introduction:
Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion. By using this he derived a formula for energy levels of electron in H-atom.
Explanation of Solution
To explain: The frequency of light used for transition from
Because of different energy spacing of both atoms, the required energy for transition from
The frequency of light used for transition from
Want to see more full solutions like this?
Chapter 7 Solutions
Bundle: General Chemistry, Loose-leaf Version, 11th + Lms Integrated For Owlv2 With Mindtap Reader, 4 Terms (24 Months) Printed Access Card
- The energy emitted when an electron moves from a higher energy state to a lower energy state in any atom can be observed as electromagnetic radiation. (a) Which involves the emission of less energy in the H atom, an electron moving from n = 4 to n = 2 or an electron moving from n = 3 to n = 2? (b) Which involves the emission of more energy in the H atom, an electron moving from n = 4 to n = 1 or an electron moving from n = 5 to n = 2? Explain fully.arrow_forwardIn X-ray fluorescence spectroscopy, a material can be analyzed for its constituent elements by radiating the material with short-wavelength X rays, which induce the atoms to emit longer-wavelength X rays characteristic of those atoms. Tungsten, for example, emits characteristic X rays of wavelength 0.1476 nm. If an electron has an equivalent wavelength, what is its kinetic energy?arrow_forwardWhich of the following is a valid set of quantum numbers for an electron in a hydrogen atom? (a) n = 1, = 0, m = 0, ms = 1 (b) n = 1, = 1, m = 0, ms = 1/2 (c) n = 1, = 0, m = 1, ms = + 1/2 (d) n = 1, = 0, m = 0, ms = 1/2arrow_forward
- 6.101 Laser welding is a technique in which a tightly focused laser beam is used to deposit enough energy to weld metal parts together. Because the entire process can be automated, it is commonly used in many large-scale industries, including the manufacture of automobiles. In order to achieve the desired weld quality, the steel parts being joined must absorb energy at a rate of about 104 W/mm2. (Recall that 1 W = 1 J/s.) A particular laser welding system employs a Nd:YAG laser operating at a wavelength of 1.06m ; at this wavelength steel will absorb about 80% of the incident photons. If the laser beam is focused to illuminate a circular spot with a diameter of 0.02 inch, what is the minimum power (in watts) that the laser must emit to reach the 104 W/mm2 threshold? How many photons per second does this correspond to? (For simplicity, assume that the energy from the laser does not penetrate into the metal to any significant depth.)arrow_forwardConsider burning ethane gas, C2H6 in oxygen (combustion) forming CO2 and water. (a) How much energy (in J) is produced in the combustion of one molecule of ethane? (b) What is the energy of a photon of ultraviolet light with a wavelength of 12.6 nm? (c) Compare your answers for (a) and (b).arrow_forwardAs the weapons officer aboard the Srarship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is 7.52 1019 J. a. What wavelength does your photon torpedo need to be to eject an electron? b. You find an extra photon torpedo with a wavelength of 259 nm and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)? c. If the hull of the enemy vessel is made of the element with an electron configura tion of [Ar]4s13d10, what metal is this?arrow_forward
- General Chemistry - Standalone book (MindTap Cour...ChemistryISBN:9781305580343Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; DarrellPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning
- Chemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage LearningChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage Learning