Concept explainers
Hydrogen
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
University Physics Volume 3
Additional Science Textbook Solutions
College Physics
College Physics (10th Edition)
Lecture- Tutorials for Introductory Astronomy
Essential University Physics: Volume 2 (3rd Edition)
Conceptual Physics (12th Edition)
Sears And Zemansky's University Physics With Modern Physics
- A diatomic molecule behaves like a quantum harmonic oscillator with the force constant 12.0 N/m and mass 5.601026kg. (a) What is the wavelength of the emitted photon when the molecule makes the transition from the third excited state to the second excited state? (b) Find the ground state energy of vibrations for this diatomic molecule.arrow_forwardAn H2 molecule can be approximated by a simple harmonic oscillator with a force constant k = 1.1 x 103 N/m. Find (a) the energy levels and (b) the possible wavelengths of photons emitted when the H2 molecule decays from the third excited state eventually to the ground state.arrow_forwardChemists use infrared absorption spectra to identify chemicals in a sample. In one sample, a chemist finds that light of wavelength 5.8 um is absorbed when a molecule makes a transition from its ground harmonic oscillator level to its first excited level. (a) Find the energy of this transition. (b) If the molecule can be treated as a harmonic oscillator with mass 5.6 * 10-26 kg, find the force constant.arrow_forward
- We are going to use Heisenberg's uncertainty principle to estimate the ground- state energy of hydrogen. In our model, the electron is confined in a one- dimensional well with a length about the size of hydrogen, so that Ax = 0.0529 nm. Estimate Ap, and then assume that the ground-state energy is roughly Ap2/2me. (Give your answer in Joules or electron-volts.)arrow_forwardA sodium atom in one of the states labeled “Lowest excited levels” in Fig. remains in that state, on average, for 1.6 * 10-8 s before it makes a transition to the ground state, emitting a photon with wavelength 589.0 nm and energy 2.105 eV. What is the uncertainty in energy of that excited state? What is the wavelength spread of the corresponding spectral line?arrow_forwardSolid metals can be modeled as a set of uncoupled harmonic oscillators of the same frequency with energy levels given by En = ħwn n = 0, 1, 2,... where the zero-point energy (the lowest energy state) of each oscillator has been adjusted to zero for simplicity. In this model, the harmonic oscillators represent the motions of the metal atoms relative to one another. The frequency of these oscillators is low so that ħw = = 224 KB and the system vibrational partition function is given by 3N Z ² = la₁ - (1 1 e-0/T). (a) If the system contains one mole of atoms, find the average energy (in J) of this system at T= 172 K. (You can use = BkB.) T (b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs expression for S, or the system partition function to make this evaluation (they are equivalent, as your reading assignment indicates).arrow_forward
- Consider photons at temperature T = 300K in a cubic box of volume 1 m' with periodic boundary conditions. a) Find the total number of photons in the lowest orbital state. What is the total energy of these photons? Hint: The 1-particle energy of photons is ɛ(k,s)=ħck = hc , independent of polarization s. Consider the Bose-Einstein distribution function (with u= 0) for the lowest-energy orbital states 2л k, = (1,0,0), k, =(0,1,0), k, =(0,0,1). Find the total number of photons that occupy L L L these states, taking into account that each of the orbital states has 2 polarizations s. b) Find the number of photons in a single orbital state with wavelength 2 = 5000 Å. What is the total energy of these photons?arrow_forwardA quantum system is described by a wave function (r) being a superposition of two states with different energies E1 and E2: (x) = c191(r)e iEit/h+ c292(x)e¯iE2t/h. where ci = 2icz and the real functions p1(x) and p2(r) have the following properties: vile)dz = ile)dz = 1, "0 = rp(x)T#(x)l& p1(x)92(x)dx% D0. Calculate: 1. Probabilities of measurement of energies E1 and E2 2. Expectation valuc of cnergy (E)arrow_forwardThe probability density function (PDF) for electrons to be detected on the x-axis between 0 nm and 1.0 nm is shown below. What is the probability of finding the electron between x = 0.5 nm and x = 1.0 nm? |w(x)* (nm') 2.0 1.0 0.5 x (nm) 1.0arrow_forward
- A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 5e-21 J apart. Use k = 1.4e-23 J/K. When the nanoparticle's energy is in the range 5(5e-21) J to 9(5e-21) J, what is the approximate heat capacity per atom?arrow_forwardWhat is the average radius of the orbit of an electron in the n=2 energy level of an oxygen atom (Z=8)? Express your answer in pico-meters.arrow_forwardAn atom in an excited state stores energy temporarily. If the lifetime of this excited state is measured to be 1.0 × 10-10 seconds, what is the minimum uncertainty in the energy of the state in eV? An atom in the excited state stores energy temporarily. If the lifetime of this excited state is measured to be 1.0 × 10-10 seconds, what is the minimum uncertainty in the energy of the state in eV?arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning