An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter A.3, Problem 15P
(a)
To determine
The energies (in eV) of the five vibrational states of a CO molecule.
(b)
To determine
The
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The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the vibrational quantum number decreases by one.
What is the effective "spring constant" for the H2 molecule in N/m ?What is the "zero point" energy (in eV) of the molecular vibration?
Consider a Face Centered Cubic (FCC) lattice structured Nickel
crystal. We are looking to find the surface energy of the new surface that is
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a-
Find the value of R as function of the lattice constant a.
4R
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Oa = 4R
Oa =
= 2/2R
V2
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04R?
O16R?
O8R?
OR?
How many atoms lie on the plane (111) within the unit cell?
N111 =
atoms within the unit cell
Find the number of atoms per unit surface area.
2
2
R2
8R2
16R?
4R?
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energt?
ON BEPA
The hydrogen iodide (HI) molecule has equilibrium separation 0.160 nm and vibrational frequency 6.93 * 1013 Hz. The mass of a hydrogen atom is 1.67 * 10-27 kg, and the mass of an iodine atom is 2.11 * 10-25 kg. (a) Calculate the moment of inertia of HI about a perpendicular axis through its center of mass. (b) Calculate the wavelength of the photon emitted in each of the following vibration-rotation transitions: (i) n = 1, l = 1 S n = 0, l = 0; (ii) n = 1, l = 2 S n = 0, l = 1; (iii) n = 2, l = 2 S n = 1, l = 3.
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An Introduction to Thermal Physics
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- An emission line of the CO molecule corresponding to a transition from its first excited state into the ground state is observed at a frequency of 115 GHz (Gigahertz). What is the wavelength of this emission line in units of mm?arrow_forwardThe two nuclei in the carbon monoxide (CO) molecules are 0.1128 nm apart. The mass of the carbon atom is 1.993x10-26 kg. The mass of the oxygen atom is 2.656x10-26 kg. Spectroscopic measurements show that adjacent vibrational energy levels for the CO molecule are 0.269 eV. What is the effective spring constant of the CO molecule? (Give your answer in N/m.)arrow_forwardThe figure shows a potential energy curve for the interaction of two neutral atoms. The two-atom system is in a vibrational state indicated by the heavy solid horizontal line. O eV -0.2 eV+ -0.4 eVF -0.6 eV -0.8 eV- -1.0 eV- -1.2 eV- -1.4 eVF -1.6 ev (a) At r = r1, what are the approximate values of the kinetic energy K, the potential energy U, and the quantity K+U? K = eV U = eV K+U = eV (b) What minimum (positive) amount of energy must be supplied to cause these two atoms to separate? eV Additi. L Matorialsarrow_forward
- The potential energy of one of the atoms in the hydrogen molecule is given by U(x) = U₁ (e-2(1-10)/b - 2e-(1-10)/b) where U₁ = 2.36 [eV], zo = 0.037 [nm], and b = 0.034 [nm]. Note that 1 [eV] = 1.6 × 10-¹⁹ [J]. Part (a) Find the energy of the hydrogen molecule in ground state. Part (b) If the measured energy of each atom in the hydrogen molecule is E= -1.15 [eV], where are the classical turning points of the atomic vibration in the hydrogen molecule?arrow_forwardThe gap between valence and conduction bands in diamond is 5.47 eV. (a) What is the maximum wavelength of a photon that can excite an electron from the top of the valence band into the conduction band? In what region of the electromagnetic spectrum does this photon lie? (b) Explain why pure diamond is transparent and colorless. (c) Most gem diamonds have a yellow color. Explain how impurities in the diamond can cause this color.arrow_forwardThe laboratory operation of a Laser is related to the atomic transition problem. Let E - E, = ho for two atomic states, u(@) be the radiation density, N be the number of atoms in state 1, and N2 that in state 2. B12 is the Enstein coffeicent for absorption, B21 that transition probability for emission, and A the spontaneous emission coefficient. Find N2/N1 O B12/[A+ B21] O B1zu(@)/[A + B21u(@)] O B1zu(@)/A O B1zu(@)/B21 O Au(@)/B12 Questio Not yet answered Marked out of P Flag question Forbidden transitions and selection rules suggest that O a photon has energy O a photon has mass O a photon has linear momentum O a photon has angular momentum a photon has parityarrow_forward
- Consider the NaCl molecule, for which the rotational inertia is 1.30x 10-45 kg*m2. If infrared radiation with wavelength 30 μ m is Raman-scattered from a free NaCl molecule, what are the allowed wavelengths of the scattered radiation?arrow_forwardIn this question, we will consider the vibration of the diatomic molecule, H2, found in an eigenstate whose wave function is 1/4 1 p(x) V48 \T where a = ku/ħ. k is the force constant and u is the reduced mass. The vibrational frequency of H2 is 4401 cm-'. а) How many nodes are present in p(x)? b) What is the quantum number that characterizes p(x)? c) Calculate the vibrational energy of the H2 molecule when it is described by the eigenfunction p(x).arrow_forwardA diatomic molecule begins in the vibration-rotation state characterized by n = 1, J = 7. It then absorbs a photon of light to make a R-branch transition. Which of the following represents a possible final state for this molecule? On=0,J = 7 n=2, J = 7 n = 1, J = 8 On=2, J = 8 n = 1, J = 6 n = 2, J = 6arrow_forward
- A sodium atom of mass 3.82 * 10^-26 kg vibrates with simple harmonic motion in crystal. The potential energy increases by 0.0075 eV when the atom is displaced 0.014 nm from its equilibrium position. Find the wavelength of a photon emitted when n=6 to n=1 transition occurs.arrow_forward(b): the potential energy of a diatomic molecule is given by U = B where A and B are constants and r is the separation A r12 r6 distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV. m² and B = 1.488 × 10-60 eV . m°. Find the separation distance at which the energy of the molecule is a %3D minimum.arrow_forward(a) Emission of microwave radiation from the J = 1→0 transition of a molecule has been detected at 88.63 GHz from a region of interstellar space in which there is evidence of thermal equilibrium and a temperature of around 20 K. Estimate the frequency and relative intensity of the J = 2 → 1 transition of the same molecule.arrow_forward
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