PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 37, Problem 10P
To determine
The reason for the room temperature an atom typically absorb
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An H2 molecule is in its vibrational and rotational ground states. It absorbs aphoton of wavelength 2.2112 µm and makes a transition to the ν = 1, J = 1energy level. It then drops to the ν = 0, J = 2 energy level while emitting6/9SIX1011a photon of wavelength 2.4054 µm. Calculate (i) the moment of inertia of theH2 molecule about an axis through its centre of mass and perpendicular tothe H − H bond, (ii) the vibrational frequency of the H2 molecule, and (iii) theequilibrium separation distance for this molecule.
A hypothetical NH molecule makes a rotational-level transition from l = 3 to l= 1 and gives off a photon of wavelength 1.780 nm in doing so. What is the separation between the two atoms in this molecule if we model them as point masses? (The mass of hydrogen is 1.67 * 10-27 kg, and the mass of nitrogen is 2.33 * 10-26 kg).
Physics
Let's look at the characteristic wavelength of radiation that is produced in molecular transitions. The separation between adjacent energy levels is typically a few eV for atomic energy levels, on the order of 0.1 eV for vibrational levels, and on the order of 10−3eV for rotational levels. Find the wavelength of the photon emitted during a transition in which the energy of the molecule decreases by 5.00 eV, 0.500 eV, and 5.00×10−3eV. In each case, in what region of the electromagnetic spectrum does the photon lie?
What is the largest energy of a transition that produces a photon in the green region of the spectrum (495 nm to 570 nm)?
Express your answer in electronvolts.
Chapter 37 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
Ch. 37 - Prob. 1PCh. 37 - Prob. 2PCh. 37 - Prob. 3PCh. 37 - Prob. 4PCh. 37 - Prob. 5PCh. 37 - Prob. 6PCh. 37 - Prob. 7PCh. 37 - Prob. 8PCh. 37 - Prob. 9PCh. 37 - Prob. 10P
Ch. 37 - Prob. 11PCh. 37 - Prob. 12PCh. 37 - Prob. 13PCh. 37 - Prob. 14PCh. 37 - Prob. 15PCh. 37 - Prob. 16PCh. 37 - Prob. 17PCh. 37 - Prob. 18PCh. 37 - Prob. 19PCh. 37 - Prob. 20PCh. 37 - Prob. 21PCh. 37 - Prob. 22PCh. 37 - Prob. 23PCh. 37 - Prob. 24PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 28PCh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 38PCh. 37 - Prob. 39PCh. 37 - Prob. 40PCh. 37 - Prob. 41PCh. 37 - Prob. 42PCh. 37 - Prob. 43P
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- A hypothetical NH molecule makes a rotational-level transition from l=3 to l=1 and gives off a photon of wavelength 1.800 nm in doing so. What is the seperation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen 1.67 * 10^-27 kg, and the mass of nitrogen is 2.33 * 10^-26 kg.arrow_forwardThe characteristic rotational energy for a diatomic molecule consisting of two idential atoms of mass 14 u (unified mass units) is 3.68 e-4 eV. Calculate the separation distance between the two atoms. Subarrow_forwardThe CO molecule makes a transition from the J = 1 to the J = 2 rotational state when it absorbs a photon of frequency 2.30 x 1011 Hz. (a) Find the moment of inertia of this molecule from these data.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_forwardThe moment of inertia of water molecule about an axis bisecting the HOH angle is1.91x10-47 kg m2. Its minimum angular momentum about that axis (other than zero) is ℏ. Inclassical terms, how many revolutions per second do the hydrogen atoms make about the axiswhen in that state? Calculate the rotational constant (cm-1) and bond length of H2O. Does the bondlength seem reasonable?arrow_forwardA hypothetical NH molecule makes a rotational-level transition from \= 3 to l = 1 and gives off a photon of wavelength 1.800 nm in doing SO. What is the separation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen is kg. 1.67 * 10-2 kg, and the mass of nitrogen is 2.33 * 10 26 a) 6.52*10^{-13}m b) 5.69*10^{-13}m c) 5.70*10^{-14} m d) 5.69*10^{-12}m e) 5.62*10^{-13}marrow_forward
- Assume the distance between the protons in the H2 molecule is 0.750 x 10-10 m. (a) Find the energy of the first excited rotational state, with J = 1. (b) Find the wavelength of radiation emitted in the transition from J = 1 to J = 0.arrow_forwardp9C.1 Familiarity with the magnitudes of overlap integrals is useful when con- sidering bonding abilities of atoms, and hydrogenic orbitals give an indication of their values. (a) The overlap integral between two hydrogenic 2s orbitals is 1 ( ZR ZR +. 2а, " 12 а, 1 + ZR 240 a, -ZR/Z0 S(2s, 2s)={1+ Plot this expression. (b) For what internuclear distance is S(2s,2s) = 0.50? (c) The side-by-side overlap of two 2p orbitals of atoms of atomic number Z is ZR 1 ( ZR ZR S(2p,2p) ={1+ 10 a, 2a, 120 a. Plot this expression. (d) Evaluate S(2s,2p) at the internuclear distance you calculated in part (b).arrow_forwardDiscuss the differences between the rotational and vibrational energy levels of the deuterium (“heavy hydrogen”) molecule D2 and those of the ordinary hydrogen molecule H2. A deuterium atom has twice the mass of an ordinary hydrogen atom.arrow_forward
- Gggarrow_forwardN 2 has a molecular weight of 28.02 g/mol a bit larger than that of a Ne atom, 20.18 g/mol. (a) At a particular temperature, Z trans= 1.90 x 10 26 for Ne in a specific container. What is the translational partition function for a N2 molecule in this container at the same temperature? (b) At 100 K, the rotational partition function for N2is found to be 17.39. What would you expect it to be at 500 K?arrow_forwardThe spacing between two adjacent lines in the pure rotational spectrum of a diatomic molecule is 20.0 cm ¹. Given KBT = 200 cm-¹ (at a specific temperature), calculate the relative population of the J-6 level O 1.6 O 3.8 O 2.7 O 2.4arrow_forward
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