Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 5, Problem 5.24P
To determine
(a)
The derivation of the expression for the wavelengths of the
To determine
(b)
The wavelengths of
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Consider the electron of a Li2+ ion that undergoes a transition from a higher energy state n to its adjacent lower energy state n – 1 (e.g. n = 2→1, 3→2, 4→3, etc) and emits a photon. Suppose the emitted photon is used to strike the surface of potassium, which has a threshold frequency of 5.464 × 10^14 s–1.a) Whatisthemaximuminitialquantumnumber,n, that is required in order to emit a photon with high enough energy to generate a photocurrent from the metal surface?b) Usingthenvaluesolvedinpart(a), calculate the maximum speed of the photoelectron from potassium. If you couldn’t solve for n in part (a), use n = 3.
Why is the following situation impossible? An experiment is performed on an atom. Measurements of the atom when it is in a particular excited state show five possible values of the z component of orbital angular momentum, ranging between 3.16 x 10-34 kg ⋅ m2/s and -3.16 x 10-34 kg ⋅ m2/s.
For 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.
Chapter 5 Solutions
Modern Physics For Scientists And Engineers
Ch. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.26PCh. 5 - Prob. 5.27P
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- What is the maximum possible angular momentum L of a hydrogen atom if its energy is -0.544 eV? Your answer should be written as a multiple of ℏ.arrow_forwardDerive an expression for the ratio of X-ray photon frequency for two elements with atomic numbers Z1 and Z2.arrow_forwardThe wavefunction for an electron in the Hydrogen atom is provided in figure 1, where B is a constant, and a0 is the Bohr radius. By inspection and using the angular part of the wavefunction, identify the value of the quantum numbers l and ml, then operate on this wavefunction with Lˆz, and use your result to verify the value of ml identified.arrow_forward
- What would the wavelength in m of the emitted radiation be if a hydrogen atom was placed in an external uniform magnetic field of 240 T and transitioned from a spin-up to a spin-down state?arrow_forwardIf the radius of the lowest energy orbit (n = 1) is 0.529 × 10-10 m, calculate the radii in m of the Bohr orbits defined by principal quantum numbers 4 and 5. (Hint use equation 1.5 and work out the overall value of the collected constants from the value of r at n = 1).arrow_forwardThe light observed that is emitted by a hydrogen atom is explained by a simple model of its structure with one proton in its nucleus and an electron bound to it, but only with internal energies of the atom satisfying EH=−RH/n2EH=−RH/n2 where RHRH is the Rydberg constant and nn is an integer such as 1, 2, 3 ... and so on. When a hydrogen atom in an excited state emits light, the photon carries away energy and the atom goes into a lower energy state. Be careful about units. The Rydberg constant in eV is 13.605693009 eV That would be multiplied by the charge on the electron 1.602× 10-19 C to give 2.18× 10-18 J A photon with this energy would have a frequency f such that E=hf. Its wavelength would be λ = c/f = hc/E. Sometimes it is handy to measure the Rydberg constant in units of 1/length for this reason. You may see it given as 109737 cm-1 if you search the web, so be aware that's not joules. The following questions are intended to help you understand the connection between…arrow_forward
- For 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_forwardFind an expression, in termsof n and the fundamental constants, for the de Broglie wavelength of an electron in the nthstate of the hydrogen atomarrow_forwardConsider a hydrogen atom in a large magnetic field. Compute the wavelengths of the photons when it transitioned from the 2p → 1s levels when the hydrogen atom is placed in a magnetic field of 2.00 Tesla. In total, consider the three transitions L=1 (2p) to L=0 (1s) associated with the three states ?ℓ= −1, 0, +1. Draw the energy levels for B=0 T and B=2 T. Ignore the effects of the intrinsic electron’s spin angular momentum and only consider the effect of the orbital angular moment L on the energy levels.arrow_forward
- A photon with a wavelength of 410 nm has energy Ephoton = 3.0 eV. Do you expect to see a spectral line with λ = 410 nm in the emission spectrum of the atom represented by this energy-level diagram? If so, what transition or transitions will emit it? Do you expect to see a spectral line with λ = 410 nm in the absorption spectrum? If so, what transition or transitions will absorb it?arrow_forwardLook up the values of the quantities in aB = h2 / 4π2 me kqe2 ,and verify that the Bohr radius aB is 0.529 x 10-10 m .arrow_forwardThe longest wavelength line of the Balmer Series for hydrogen occurs at 656.3 nm corresponding to the transition from n2 = 3 to n1 = 2. Determine the value for the Rydberg constant for hydrogen using these values.arrow_forward
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