SA2. In the hydrogen atom we discussed the concept of spatial quantization where the electron can have only certain values of orbital angular momentum with its magnitude given by ||=√√(l + 1)ħ. Explain in your own words why, given the Heisenberg uncertainty relationships, the magnitude of the orbital angular momentum CANNOT be given by | | = lħ.
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- a) [2018] State Kirchhoff’s two Laws, and give the fundamental physical principles which each law expresses. b) De Broglie explained the Bohr model of the hydrogen atom by attributing a wavelength λ toa particle, with the value of λ coming from the momentum p = mv as λ = h/p.i) Calculate the de Broglie wavelength of a bird (a racing pigeon) that weighs 0.350 kgand flies at 100 km per hour.ii) Equating the centripetal force on an electron orbiting around a proton with the Coulomb force gives the expression v2 = e2/(4πε0mer). Calculate the speed of an electron or- biting at the Bohr radius, rB = 0.053 nm.iii) Calculate the momentum and the de Broglie wavelength of an electron moving at the speed you obtain in (ii).iv) Compare the wavelength you obtain in (iii) with the circumference of the orbit. Com- ment on this comparison. Explain briefly what it implies about the possible orbits of the Bohr model and how the higher orbits might be predicted. c) Thorium-234 is…An electron is in an f state. Can it undergo a quantum jump to an s state? A p state? A d state? Explain.12QM. Please answer question throughly and detailed.
- 1) An electron is confined to a square box of length L, and the walls of that box are infinitely high. The zero-point energy (ZPE) is defined as the minimal energy that corresponds to the smallest quantum number n. What would be the length of the box L such that the ZPE of the electron located inside this box is equal to its rest mass energy mec2?3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) What is the most probable radius (in terms of a,) at which the electron is found? (c) What is the expectation value of r in this state? Note: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note:3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.
- i know the answer is NOT 9.42(10^-21)GggPhysics 1. Derive the expression ε(ω)=1- ωp 2 / ω2 , ωp2 =ne2 /ε0m for the dielectric constant as a function of ω for a free electron gas of number density n. 2. Show clearly that metals are opaque to light for which ω is less than ωp. 3. Calculate the wavelength cutoff for Na metal if the volume of a primitive unit cell in Na is 35×10-30 m3 how to solve this problem?
- an electron in a hydrogen atom is in a state with principal quantum number n = 3. a) what is the largest orbital angular momentum it can have? b) which values of the z - component of the angular momentum are allowed with this total momentum? (leave answers in units of h bar) c) the electron transitions to the n = 2 energy level, emitting a photon. what is that photon's length?= 1. Photoelectric effect. In a photoelectric experiment in which monochromatic light of wave- length \ falls on a potassium surface, it is found that the stopping potential Vstop is 1.9 V for > 300 nm and 0.88 V for \ = 400 nm. Imagine we know neither Planck's constant, nor the workfunction for potassium, nor the threshold frequency fo. But assume we do know the elementary charge e 1.60 × 10-19 C and want to test the theoretical prediction of Eintsein's theory. = (a) From the given data, calculate a value for Planck's constant, h. (b) From the same data, find the workfunction Eo and the threshold frequency fo for potas- sium. (c) Then compare your results for h and Eo to their known values (see Knight, Table 38.1 for the work function). (d) Plot eVstop as a linear function of frequency f. Include the information you have found in parts (a) and (b) as well as the experimental data.