Concept explainers
Light Energy, and the Hydrogen Atom
- a Which has the greater wavelength, blue light or red light?
- b How do the
frequencies of blue light and red light compare? - c How does the energy of blue light compare with that of red light?
- d Does blue light have a greater
speed than red light ?- e How does the energy of three photons from a blue light source compare with the energy of one photon of blue light from the same source? How does the energy of two photons corresponding to a wavelength of 451 nm (blue light) compare with the energy of three photons corresponding to a wavelength of 704 nm (red light)?
- f A hydrogen atom with an electron in its ground state interacts with a photon of light with a wavelength of 1.22 × 10−6 m. Could the electron make a transition from the ground state to a higher energy level? If it does make a transition, indicate which one. If no transition can occur, explain.
- g If you have one mole of hydrogen atoms with their electrons in the n = 1 level, what is the minimum number of photons you would need to interact with these atoms in order to have all of their electrons promoted to the n = 3 level? What
wavelength of light would you need to perform this experiment?
(a)
Interpretation:
The light with higher wavelength has to be identified from the given lights.
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
Answer to Problem 7.23QP
Red light has larger wavelength than blue light.
Explanation of Solution
To identify: The light with higher wavelength.
Wavelength and frequency are inversely proportional to each other. Frequency of blue light is higher than red light. Thus, red light has larger wavelength than blue light.
By using the relation between wavelength and frequency, the light with higher wavelength was identified.
(b)
Interpretation:
The light with higher frequency has to be identified from the given lights.
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
Answer to Problem 7.23QP
Blue light has larger frequency than red light.
Explanation of Solution
To identify: The light with higher frequency.
Wavelength and frequency are inversely proportional to each other. Wavelength of blue light is less than red light. Thus, blue light has larger frequency than red light.
By using the relation between wavelength and frequency, the light with higher frequency was identified.
(c)
Interpretation:
The energies of blue light and red light has to be related.
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
Answer to Problem 7.23QP
Blue light has higher energy than red light.
Explanation of Solution
To compare: The energy of blue light and red light.
Energy and frequency are directly proportional to each other. Frequency of blue light is higher than red light. Thus, blue light has higher energy than red light.
By using the relation between wavelength and frequency, the energy of blue light and red light was related.
(d)
Interpretation:
The speed of blue light and red light has to be compared.
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
Answer to Problem 7.23QP
Blue light has higher energy than red light.
Explanation of Solution
To compare: The speed of blue light and red light.
Energy and frequency are directly proportional to each other. Frequency of blue light is higher than red light. Thus, blue light has higher energy than red light.
By using the relation between wavelength and frequency, the energy of blue light and red light was related.
(e)
Interpretation:
The energy of one photon and energy of three photons of blue light has to be compared.
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
Answer to Problem 7.23QP
Blue light (
Explanation of Solution
To compare: The energy of one photon and energy of three photons of blue light.
Blue light with energy of three photons is thrice the energy of one photon. In order to relate the energy of two photon (blue light) with energy of three photon (red light), the energy is given as
Blue light (
By using the relation between wavelength and frequency, the energy of two photon of blue light and energy of three photons of red light was related.
(f)
Interpretation:
The possibility of transition of an electron of hydrogen atom from ground state to higher energy state has to be determined.
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
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 7.23QP
The obtained energy for transition is greater than the energy of light. Therefore, no transition occurs.
Explanation of Solution
To determine: The possibility of transition of an electron of hydrogen atom from ground state to higher energy state.
By using the below formula and calculate frequency and energy of light
The minimum energy required for the transition of
The obtained energy for transition is greater than the energy of light. Therefore, no transition occurs.
The possibility of transition of an electron of hydrogen atom from ground state to higher energy state was determined.
(g)
Interpretation:
The energy required for transition of an electron of hydrogen atom from
Concept introduction:
Relation between frequency and wavelength is,
C is the speed of light.
h is Planck’s constant (
E is energy of light particle.
Wavelength and frequency are inversely proportional to each other.
The distance between any two similar points of a wave is called wavelength
Figure 1
Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.
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 7.23QP
The minimum energy required for the transition of
The wavelength of the light is
Explanation of Solution
To determine: The energy required for transition of an electron of hydrogen atom from
The minimum energy required for the transition of
The energy required for transition of an electron of hydrogen atom from
Want to see more full solutions like this?
Chapter 7 Solutions
Bundle: General Chemistry, Loose-leaf Version, 11th + OWLv2, 4 terms (24 months) Printed Access Card
- Consider the transition from the energy levels n=5 to n=3. (a) What is the frequency of light associated with this transition? (b) In what spectral region does the transition occur? (c) Is energy absorbed?arrow_forwardExplain the hydrogen emission spectrum. Why is it significant that the calm emitted is not while? How does the emission spectrum support the idea of quantized energy levels?arrow_forwardWhich statement is true of the quantum mechanical model, but not of the Bohr model? a. Electrons orbit the nucleus in simple circular orbits, just like planets orbit the Sun. b. The exact path that an electron follows within an atom cannot be specified. c. The electron is attracted to the nucleus of the atom.arrow_forward
- Ozone absorbs energy with a frequency of 1.291015 s1. (a) What is the wavelength (in nm) of the absorption? (b) In what spectral range does the absorption occur? (c) What is the energy absorbed by one photon?arrow_forwardDetermine whether each statement that follows is true or false: a Electron energies are quantized in excited states but not in the ground state. b Line spectra of the elements are experimental evidence of the quantization of electron energies. c Energy is released as an electron passes from ground state to an excited state. d The energy of an electron may be between two quantized energy levels. e The Bohr model explanation of line spectra is still thought to be correct. f The quantum mechanical model of the atom describes orbitals in which electrons travel around the nucleus. g Orbitals are regions in which there is a high probability of finding an electron. h All energy sublevels have the same number of orbitals. i The 3p orbitals of an atom are larger than its 2p orbitals but smaller than its 4p orbitals. j At a given sublevel, the maximum number of d electrons is 5. k The halogens are found in Group 7A/17 of the periodic table. l The dot structure of the alkaline earths is X, where X is the symbol of element in the family. m Stable ions formed by alkaline earth metals are isoelectronic with noble gas atoms. n Atomic numbers 23 and 45 both belong to transition elements. o Atomic number 52, 35, and 18 are arranged in order of increasing atomic size. p Atomic number 7, 16, and 35 are all nonmetals.arrow_forwardWhat is the difference between an atom’s ground state and an excited state?arrow_forward
- now have evidence that electron energy levels in atoms are quantized. What if energy levels in atoms were not quantized? What are some differences we would notice?arrow_forwardIn the Bohr model of the hydrogen atom, the electron occupies distinct energy states. In one transition between energy states, an electron moves from n=1 to n=2. Is energy absorbed or emitted in the process? Does the electron move closer to or farther from the nucleus?arrow_forwardThe Bohr model works for only one electron species. Why do we discuss it in this text (what's good about it)?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 LearningIntroductory Chemistry: An Active Learning Approa...ChemistryISBN:9781305079250Author:Mark S. Cracolice, Ed PetersPublisher:Cengage LearningWorld of Chemistry, 3rd editionChemistryISBN:9781133109655Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCostePublisher:Brooks / Cole / Cengage Learning
- Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning