EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 39, Problem 12P
To determine
The proof that the ground-state wave function
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(A) An electron is confined between two impenetrable walls 0.200 nm apart. Determine the energy levels for the states n = 1, 2, and 3.
(4) Electronic energy level of a hydrogen atom is given by
R
; п %3D 1,2, 3,...
n2
E = -
and R = 13.6 eV. Each energy level has degeneracy 2n2 (degeneracy is the number of equivalent
configurations associated with the energy level).
(a) Derive the partition function for a hydrogen atom at a constant temperature.
(b) Consider that the energy level of a hydrogen atom is approximated by a two level system,
n = 1,2. Estimate the mean energy at 300 K.
Prove that the density of states is the same size
and the wavelength range of
a + da toa
to be
g(1)da :
%3!
Chapter 39 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 39 - Prob. 2QCh. 39 - Prob. 3QCh. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11P
Ch. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46P
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- (1)Earlier in class, we said that the electronic states of the π electrons of a conjugated linear-like molecule could be approximated by the wave functions of a particle in a one-dimensional box of length L A) Write down the wave function for a single electron for such a system. Include any restrictions on the quantum number(s). B) Show that the transition probability with x-polarized light for the transition n = 1 → n = 2 is non-zero. C) Show that the transition probability with x-polarized light for the transition n = 1 → n = 3 is zero. D) What wavelength of photon is required for the transition in part (b) to occur? Assume that the excitation process is a one-photon process. please answer all parts as they pertain to each other.arrow_forwardAn atom, with atomic mass A = 22 is trapped in a harmonic oscillator with angular frequency 24.5 rad/s. If the atom is cooled into its quantum ground state, what is the spatial rms width Δx (in microns) of its Gaussian probability distribution? [Δx is similar to a classical standard deviation]arrow_forward(a) Write the expression of average no. of particle (s) in particular single particle quantum state (s) for a quantum gas of N identical particle at temp. T. If partilcle is fermion then show that- Here B - ns = 1 kT 1 ea+Bei +1 energy of state.arrow_forward
- (a) Show that the total number of atomic states (including different spin states) in a shell of principal quantum number n is 2n2. (b) Which shell has 50 states?arrow_forwardA proton is confined in box whose width is d = 750 nm. It is in the n = 3 energy state. What is the probability that the proton will be found within a distance of d/n from one of the walls? [Hint: the average value sin2x over one or more of its cycles is 1/2.] Include a sketch of U(x) and ?(x).arrow_forward(b) Explain the working principle of laser photon emission by using the concepts “population inversion”, “stimulated emission” and corresponding energy-band diagrams.arrow_forward
- i) Consider the anomalous Zeeman pattern of D1 and D2 lines of sodium. Calculate the frequency of the component of D₁ line corresponding to Am, = +1 where Am, = m - m (Double prime represent lower state).arrow_forward(a) Using the microscopic cross sections from Hubbel et al (1975), calculate the mass attenuation coefficients for Compton scattering from the following elements: U, W, Pt, Fe and Al at the following energies: 0.1, 0.5, and 1 MeV.arrow_forwardConsider the electron-hole overlap integral Mnn for a quantum well given by: Mn Pen (2) Pnn (z) dz. %3D - 00 n' and zerd (i) Show that Mon is unity if n otherwise in a quantum well with infinite barriers. (ii) Show that Mon is zero if (n-n') is an odd number in a quantum well with finite barriers.arrow_forward
- An electron is in a spin state given by 2 to = √² (¹/²) |x) 3 Find the probability that a measurement of Sy will yield the value +ħ/2.arrow_forwardThe energy spectrum of a particle consists of four states with energies 0,e, 2 e,3 e. Let Z, (T),Z, (T) and Ze(") denote the canonical partition functions for four non- interacting particles at temperature T. The subscripts B, F and C corresponds to bosons, fermions and distinguishable classical particles, respectively. Let y= exp k„T Which one of the following statements is true about ZB (T), ZF (T) and Zc (T)? (a) They are polynomials in y of degree 12,6 and 12, respectively. (b) They are polynomials in y of degree 16,10 and16, respectively (c) They are polynomials in y of degree 9,6 and 12, respectively. (d) They are polynomials in y of degree 12,10 and 16, respectively.arrow_forwardif the chlorine molecule at 290K were to rotate at the angular frequency predicted by the equipartition theorem what would be the average centipital force ? ( the atoms of Cl are 2 x 10-10 m apart and the mass of the chlorine atom 35.45 a.m.u )arrow_forward
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