University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 41.2, Problem 41.2TYU
To determine
To Rank: The following states of a particle in a cubical box of side
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Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3.
(a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L.
(b) Which if these energies are degenerate?
Show that for transitions between any two n states of atomic hydrogen, no more than three different spectral lines can be obtained for the normal Zeeman effect.
For a hydrogen atom, determine the allowed states corresponding to the principal quantum number n = 2 and calculate the energies of these states.
Chapter 41 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 41.1 - Prob. 41.1TYUCh. 41.2 - Prob. 41.2TYUCh. 41.3 - Prob. 41.3TYUCh. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYUCh. 41.7 - Prob. 41.7TYUCh. 41.8 - Prob. 41.8TYUCh. 41 - Prob. 41.1DQCh. 41 - Prob. 41.2DQ
Ch. 41 - Prob. 41.3DQCh. 41 - Prob. 41.4DQCh. 41 - Prob. 41.5DQCh. 41 - Prob. 41.6DQCh. 41 - Prob. 41.7DQCh. 41 - In the ground state of the helium atom one...Ch. 41 - Prob. 41.9DQCh. 41 - Prob. 41.10DQCh. 41 - Prob. 41.11DQCh. 41 - Prob. 41.12DQCh. 41 - Prob. 41.13DQCh. 41 - Prob. 41.14DQCh. 41 - Prob. 41.15DQCh. 41 - Prob. 41.16DQCh. 41 - Prob. 41.17DQCh. 41 - Prob. 41.18DQCh. 41 - Prob. 41.19DQCh. 41 - Prob. 41.20DQCh. 41 - Prob. 41.21DQCh. 41 - Prob. 41.22DQCh. 41 - Prob. 41.23DQCh. 41 - Prob. 41.1ECh. 41 - Prob. 41.2ECh. 41 - Prob. 41.3ECh. 41 - Prob. 41.4ECh. 41 - Prob. 41.5ECh. 41 - Prob. 41.6ECh. 41 - Prob. 41.7ECh. 41 - Prob. 41.8ECh. 41 - Prob. 41.9ECh. 41 - Prob. 41.10ECh. 41 - Prob. 41.11ECh. 41 - Prob. 41.12ECh. 41 - Prob. 41.13ECh. 41 - Prob. 41.14ECh. 41 - Prob. 41.15ECh. 41 - Prob. 41.16ECh. 41 - Prob. 41.17ECh. 41 - Prob. 41.18ECh. 41 - A hydrogen atom in a 3p state is placed in a...Ch. 41 - Prob. 41.20ECh. 41 - Prob. 41.21ECh. 41 - Prob. 41.22ECh. 41 - Prob. 41.23ECh. 41 - Prob. 41.24ECh. 41 - Prob. 41.25ECh. 41 - Prob. 41.26ECh. 41 - Prob. 41.27ECh. 41 - Prob. 41.28ECh. 41 - Prob. 41.29ECh. 41 - (a) Write out the ground-state electron...Ch. 41 - Prob. 41.31ECh. 41 - Prob. 41.32ECh. 41 - Prob. 41.33ECh. 41 - Prob. 41.34ECh. 41 - Prob. 41.35ECh. 41 - Prob. 41.36ECh. 41 - Prob. 41.37ECh. 41 - Prob. 41.38ECh. 41 - Prob. 41.39PCh. 41 - Prob. 41.40PCh. 41 - Prob. 41.41PCh. 41 - Prob. 41.42PCh. 41 - Prob. 41.43PCh. 41 - Prob. 41.44PCh. 41 - Prob. 41.45PCh. 41 - Prob. 41.46PCh. 41 - Prob. 41.47PCh. 41 - Prob. 41.48PCh. 41 - Prob. 41.49PCh. 41 - Prob. 41.50PCh. 41 - Prob. 41.51PCh. 41 - Prob. 41.52PCh. 41 - Prob. 41.53PCh. 41 - Prob. 41.54PCh. 41 - Prob. 41.55PCh. 41 - Prob. 41.56PCh. 41 - Prob. 41.57PCh. 41 - Effective Magnetic Field. An electron in a...Ch. 41 - Prob. 41.59PCh. 41 - Prob. 41.60PCh. 41 - Prob. 41.61PCh. 41 - Prob. 41.62PCh. 41 - Prob. 41.63PCh. 41 - Prob. 41.64PCh. 41 - Prob. 41.65PCh. 41 - Prob. 41.66PCh. 41 - Prob. 41.67PCh. 41 - Prob. 41.68CPCh. 41 - Prob. 41.69CPCh. 41 - Prob. 41.70PPCh. 41 - Prob. 41.71PPCh. 41 - Prob. 41.72PPCh. 41 - Prob. 41.73PP
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Similar questions
- Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).arrow_forwardFor a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .arrow_forwardConsider a quantum mechanical ideal harmonic oscillator having a zero point energy of 1.4*10^-20J. how much energy could be released if the oscillator makes a transition from n=4 to n=2 states? a)0.69*10^19J b)2.88*10^-20J c)5.76*10^20J d)none are correctarrow_forward
- Enumerate all states of the hydrogen atom corresponding to the principal quantum number n = 2, giving the spectroscopic designation for each. Calculate the energies of these states.arrow_forwardShow that the number of states with the same quantum number n is 2n2arrow_forwardFor what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.0 mm? Assume that l has its maximum value of n - 1.arrow_forward
- A rectangular corral of widths Lx= L and Ly = 2L containsseven electrons. What multiple of h2/8mL2 gives the energy of theground state of this system? Assume that the electrons do not inter-act with one another, and do not neglect spin.arrow_forwardWhich of the following set of quantum numbers (ordered n, ℓ, mℓ, ms) are possible for an electron in an atom? Check all that apply. 4, 2, 1, -1/2 3, 2, 2, -1/2 3, 3, 1, -1/2 5, 3, 4, 1/2 3, 2, 0, -2 3, 1, -2, -1/2 5, 3, -3, 1/2 -3, 2, 2, -1/2arrow_forwardA 10 g marble is in a 1-D box of 10 cm. Assuming infinitely hard walls, (a) find its permitted energies (in J) and (b) the corresponding quantum number for the marble moving at 30 cm/s.arrow_forward
- Consider a head-on collision between two hydrogen atoms, both initially in their ground state and moving with the same speed. Find the minimum speed necessary to leave both atoms in their n = 4 state after the collisionarrow_forwardA simple illustration of the variation method is provided by the hydrogen atom in the 1s state. Let us assume a form of the trial wave function ψ=e–br where b is a constant. For hydrogen atom, V=-e2/r, so the Hamiltonian operator is Ĥ=-h2/8π2m V2- e2/r.The energy depends on r for the 1s state of the hydrogen atom so the angular portion of the Laplacian can be omitted and replaced by the factor 4π after integration. Therefore, the radial portion of V2=1/r2 (∂/∂r) r2 ∂/∂r. Solve the energy minimum of the hydrogen atom, E = -2π2 me4/h2.arrow_forwardThe radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}( 2 - r/a ) exp(-r/2a), where a is the Bohr radius.(a) Sketch the graph of R(r) x r. For a decent sketch of this graph, take into account some values of R(r) at certain points of interest, such as r=0, 2a, 4a, and so on. Also take into account the extremes of the function R(r) and their inflection points, as well as the limit r--> infinity.arrow_forward
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