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Concept explainers
(a)
Interpretation:
The energy difference in
Concept introduction:
The energy of the harmonic oscillator is given by,
Where,
•
•
•
•
The total energy of the harmonic oscillator depends on the classical frequency and the integer
(b)
Interpretation:
The
Concept introduction:
The energy of the harmonic oscillator is given by,
Where,
•
•
•
•
The total energy of the harmonic oscillator depends on the classical frequency and the integer
(c)
Interpretation:
The region of the
Concept introduction:
Electromagnetic spectrum is the classification of the electromagnetic radiation according to their frequencies and wavelengths. This spectrum consists of gamma rays, X-rays, ultraviolet rays, visible region, microwaves and radio waves.
(d)
Interpretation:
An explanation of the results of parts a and b on the basis of the state of science in the early twentieth century is to be stated.
Concept introduction:
The energy of the harmonic oscillator is given by,
Where,
•
•
•
•
The total energy of the harmonic oscillator depends on the classical frequency and the integer
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Chapter 11 Solutions
Physical Chemistry
- Show that the value of the Rydberg constant per photon, 2.179 1018 J, is equivalent to 1312 kJ/mol photons.arrow_forward6.9 If a string of decorative lights includes bulbs with wave-lengths of 480, 580, and 700 mm, what are the frequencies of the lights? Use Figure 6.6 to determine which colors are in the set.arrow_forwardWhat experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?arrow_forward
- Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.arrow_forward(i) What do you understand by the dual nature of light? Explain clearly in few sentences. (ii)What is the difference between an emission and an absorption spectra? (iii) What is meant by Heisenberg uncertainty principle? Explain clearly in as simple a language as possible. (iv)What are the quantum numbers? How many are there ? What are their symbols and what do they signify? (v)What do you mean by periodic properties? What are the different trends seen in a periodic table and how can you explain them in at least two to three simple sentences for each of them?arrow_forward(a) What is the lowest possible value of the principal quantum number (n) when the angular momentum quantum number (ℓ) is 1? (b) What are the possible values of the angular momentum quantum number (ℓ) when the principal quantum number (n) is 4 and the magnetic quantum number (mℓ) is 0?arrow_forward
- (a) The first step in ozone formation in the upper atmosphere occurs when oxygen molecules absorb UV radiation of wave-lengths ≤242 nm. Calculate the frequency and energy of theleast energetic of these photons. (b) Ozone absorbs light having wavelengths of 2200 to 2900 Å, thus protecting organisms on Earth’s surface from this high-energy UV radiation. What are the frequency and energy of the most energetic of these photons?arrow_forwardIt is interesting to speculate on the properties of a universe with different values for the fundamental constants.(a) In a universe in which Planck’s constant had the valueh =1 J s, what would be the de Broglie wavelength ofa 145-g baseball moving at a speed of 20 m s-1 ?(b) Suppose the speed of the ball from part (a) is known to lie between 19 and 21 m s-1. What is the smallest distance within which it can be known to lie?(c) Suppose that in this universe the mass of the electron is1 g and the charge on the electron is 1 C. Calculate the Bohr radius of the hydrogen atom in this universe.arrow_forwardAtomic hydrogen produces several series of spectral lines. Each series fits the Rydberg equation with its own particular n1 value. Calculate the value of n1 (by trial and error if necessary) that would produce a series of lines in which:(a) The highest energy line has a wavelength of 3282 nm.(b) The lowest energy line has a wavelength of 7460 nm.arrow_forward
- A hydrogen atom is in the 3d state. (a) What is the magnitude of the electron's orbital angular momentum? (b) What are the possible values for the magnetic quantam number, ml and the magnetic spin number, ms? (c) If the hydrogen atom is in the 3d state and falls back to the ground state, what wavelength would be emitted?arrow_forwardPhotons of wavelength 315 nm or less are needed to eject electrons from a surface of electrically neutral cadmium.(a) What is the energy barrier that electrons must overcome to leave an uncharged piece of cadmium?(b) What is the maximum kinetic energy of electronsejected from a piece of cadmium by photons of wavelength 200 nm?(c) Suppose the electrons described in (b) were used ina diffraction experiment. What would be their wavelength?arrow_forwardThe Lyman series of the hydrogen atom represents transitions from the electronic energy level n to the energy level n=1. (i) Derive a formula that relates (a) the transition energy, AE, and (b) the wavelength, >, of the emitted photon to the quantum number of the upper energy level n. (ii) Calculate the expected wavenumber, , for the first 4 transitions in the Lyman series.arrow_forward
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