Chapter 5, Problem 18Q

a. For the allowed energies of a particle in a box to be large, should the box be very big or very small? Explain.b. Which is likely to have larger values for the allowed energies: an atom in a molecule, an electron in an atom, or a proton in a nucleus? Explain.

a) How many ways are there to arrange 3 quanta among 4 atoms in a solid? b) . the ground state energy. What is the Boltzmann factor for this excited state? >At room temperature, the fourth excited state of a microscopic oscillator is o.6 eV above

Consider the Balmer series discussed in the book (and Prof. Scherer's lecture notes), where the frequencies are given by: x (3.29 × 1015 s-1) n = 3,4,5, .. v = Let us focus only on the spectral lines and transitions corresponding to the Balmer series. a) Suppose the Balmer series of hydrogen is studied using a Franck-Hertz experiment. What is the threshold voltage required for n=3? How about n=4? b) The Lyman Series frequencies are given by v = |1- x (3.29 x 1015 s-1). Describe what is different about these two series of emission frequencies of photons from the hydrogen atom? That is, what distinguishes one series from the other? (Hint: it may help to think about the Bohr model interpretation of transitions.)

Q1: Consider the ideal laser medium behaves as a four-level system and the population inversion between states 2 and 3. The pump excites the atoms to states 3 and 2 at a rate pumping R3 and R₂, respectively. State 4 decays back to 3 so fast. What is the pump rate in the absence of the saturating beam and no oscillation on the state 3? Assume that the degeneracies in all states are different.

The radial wave function for the 5f orbital can be expressed as: Rn (r) = Ne-r/5 p3 (8-4) where N is a normalization constant. a. What is n? n = a. What is l? = c. How many nodes does this wave function have? # nodes= d. Compute the numerical value of the integral Jo I 2 Rn,Kr) Rn,(r) dr :

AI answered the problem this way. Is this correct?  From the text you've provided, it seems like the problem at hand is to calculate the wavelength of a photon emitted when singly ionized helium (He+) transitions from the n=3n=3 to n=2n=2 state. Since He+ is a single-electron ion, it behaves like a hydrogen atom, so we can apply the same equations and principles. The text mentions the Balmer series, which corresponds to transitions to n=2n=2. The Balmer-alpha line, often referred to as the Hydrogen-alpha or Hα line, corresponds to the transition from n=3n=3 to n=2n=2 in hydrogen, and its wavelength is 656 nm. Since the helium ion (He+) behaves similarly to hydrogen in this context, the answer to the problem would also be 656 nm. The emitted photon has a wavelength of 656 nm.

Which of the following statements related to quantum statistics are true? Select one or more: a.The wave function of a pair of bosons is symmetric with respect to the exchange of particles. b.If the particle density of an ideal gas is very low (that is, the particle density is much less than the cube of the thermal de Broglie wavelength), quantum effects are important. c.In the case of a rare gas and at high enough temperatures, the Fermi-Dirac and Bose-Einstein distributions are approximately the same. d.Two bosons cannot be in the same quantum state.

Solve the following problem: Use rest mass energy of the electron 0.5 MeV Consider an atomic level with quantum numbers n = 2,l = 1 and maximum total angular momentum. a. Find the first order relativistic correction to this level, in electron- volts. b. Find the first order spin-orbit correction to this level, in electron-volts. C. Use your result in parts a and b to find the energy of that level.

(a) What is the minimum value of l for a subshell that contains 11 electrons? (b) If this subshell is in the n = 5 shell, what is the spectroscopic notation for this atom?