Show that the third Bohr postulate, Eq. (2-5), is equivalent to an integer num- ber of de Broglie waves fitting within the circumference of a Bohr circular orbit.
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- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.To what speed must a proton be accelerated from rest for it to have a de Broglie wavelength of 100 pm? What accelerating potential difference is needed?
- Describe and justify the Born interpretation of the wavefunction.To what speed must an electron be accelerated from rest for it to have a de Broglie wavelength of 100 pm? What accelerating potential difference is needed?For the system described in Exercise E7C.8(a), evaluate the expectation value of the angular momentum represented by the operator(ħ/i)d/dϕ for the case ml = +1, and then for the general case of integer ml.
- Without evaluating any integrals, state the value of the expectation value of x for a particle in a box of length L for the case where the wavefunction has n = 2. Explain how you arrived at your answer.Which of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);(ii) cos(ax) e-x^2? Which of these functions are acceptable as wavefunctions?What is the relation between the Debye length and the zeta potential?
- Calculate the molar heat capacity of a monatomic non-metallic solid at 500 K which is characterized by an Einstein temperature of 300 K. Express your result as a multiple of 3R.By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a particle in a ring with different values of the quantum number ml are mutually orthogonal.