Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 8.2, Problem 8.7P
To determine
The ionization energy for the helium.
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Calculate the speed of the electron in a hydrogen atom in the state n = 5, in m/s. Express your answer as vx
10° m/s and type in just the value of v. Use three decimals in your answer.
Ex. 8: Calculate the energy of the electron in
the first orbit in a hydrogen atom. Express the
answer in electron volt.
In the relativistic treatment of the hydrogen atom (excluding QED), the 251/2 and 2P1/2 levels are found to be degenerate. Which of the
following best describes why?
Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.
a The degeneracy is a result of the rotational symmetry of the H-atom
b
d
e
The Darwin and spin-orbit terms exactly cancel for both levels
Each individual contribution (mass-velocity, Darwin and spin-orbit) to the splitting only depend on the total angular momentum
quantum number j
The mass-velocity and Darwin terms exactly cancel for both levels
The degeneracy is due to a subtle symmetry of a 1/r potential when n = 1 and would no longer be the case for other n.
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Introduction To Quantum Mechanics
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- A hydrogen atom ¹H with 200 eV of kinetic energy has a head-on, perfectly elastic collision with a ¹2C atom at rest. Part A Afterward, what is the kinetic energy, in eV, of ¹H? Express your answer in electron volts. KfH = Submit Part B V Kfc = ΑΣΦ Request Answer Afterward, what is the kinetic energy, in eV, of ¹2C? Express your answer in electron volts. ww ΑΣΦ ? ? eV eVarrow_forwardChapter 39, Problem 043 In the ground state of the hydrogen atom, the electron has a total energy of -13.6 ev. What are (a) its kinetic energy and (b) its potential energy if the electron is a distance 4.0a from the central nucleus? Here a is the Bohr radius. (a) Number Units eV (b) Number Units eVarrow_forward13.10 If the radial momentum p, and radial velocity a, for an electron in a central potential are defined by r.p-ih a.r Pr = Xr= " r r show that ihk Ba, (ap) = ar Pr + r B(o'. L + h) where k = ħarrow_forward
- So Determine the distance between the electron and proton in an atom if the potential energy ?U of the electron is 15.4 eV (electronvolt, 1 eV =1.6×10−19=1.6×10−19 J). Give your answer in Angstrom (1 A = 10-10 m)arrow_forwardUse the Saha equation to determine the fraction of Hydrogen atoms that are ionized Nu/Ntotal at the center of the Sun, where the temperature is 15.7 million K and the electron number density is ne=6.1x1031 /m³. Don't try to compare your result with actual data, as your result will be lower due to not taking the pressure into account. Since most of the neutral H atoms are in the ground state, use Zrdegeneracy3D2 and, since a H ion is just a proton, Zı=1. Also, use XI=13.6 eV.arrow_forwardProblem 1. Two State System Consider an atom with only two states: a ground state with energy 0, and an excited state with energy A. Determine the mean energy (e) and variance in energy (de). Sketch the mean energy versus A/k T.arrow_forward
- A Construct the wavefunction V(r, 0, ¢) for an H atoms' electron in the state 2pz. Please note that in order to have a real-valued wavefunction of pr orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction. Px 1/2 Yg = ()"" (5 cos 0 -3 cos 0) cos e %3D (4x 21 12 64л/ 1/2 sin e (5 cos? e- 1)eti 87 -y Y = (3 cos²0 – 1) 105 1/2 32 sin e cos de2ie (167 15 12 sin e cos betie 35 12 (647 sin de i B Now consider an excited state of He atom with electron configuration 1s 2s'. In general, the wavefunction is a state: V(r, 0, 0, 02) = V(r,0, ø)V.. where V(r, 0, 6) and V,, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, ø) and o (r, 0,…arrow_forward▼ Part A For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ap at distance aB? ▸ View Available Hint(s) 15. ΑΣΦ ? Part B For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ag at distance ag from the proton? ▸ View Available Hint(s) [5] ΑΣΦ ? Submit Submitarrow_forwardDerive the rn, vn and En the quantized parameters for a hydrogen-like atom with a number of protons that you will keep in your derivation of the answers as Z. Note:1) An example of the situation would for instance He+ with one single electron left to orbit the nucleus of Helium or Li++ with one single electron left to orbit the nucleus of Lithium.arrow_forward
- The Lennard-Jones parameters for argon are: A = 1.022 x 10-7 J m° and B = 1.579 x 10-134 J m12. Calculate the distance at which the energy will be minimum and calculate the minimum energy. Draw the energy profile also. I.arrow_forwardDetermine the distance between the electron and proton in an atom if the potential energy U of the electron is 10.1 eV (electronvolt, 1 eV = 1.6 × 10-19 J). Give your answer in Angstrom (1 A = 10-10 m). Answer: Choose... +arrow_forwardE Suppose an electron is in the ground state of hydrogen. (a) Whatis the highest-energy photon this system can absorb without dissociating the electron from the proton? Explain. (b) What is thelowest-energy photon this system can absorb? Explainarrow_forward
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