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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Ex. 8: Calculate the energy of the electron in
the first orbit in a hydrogen atom. Express the
answer in electron volt.
Problem 7: The electric potential near a hydrogen atom can
be modeled as the equation to the right where ao is the Bohr
radius and q is the charge on the central proton.
V (r)
exp(- 2r/a,)(1 +a/r)
Randomized Variables
m = 2
n = 3
Part (a) Find an expression for the 0-component of the electric field, Eg.
Numeric : A numeric value is expected and not an expression.
Eg =
Part (b) Find an expression for the o-component (azimuthal) of the electric field, Eo
Expression :
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, a, b, c, d, g, h, j, k, m, P, S, t
Part (c) What is the change in the magnitude of the electric field (in N/C) if a test point moves from the position (x = m²ao, y
= 0, z = 0) to position (x = n-ao, y = 0, z = 0).
Numeric : A numeric value is expected and not an expression.
ΔΕ Ξ
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.
Chapter 8 Solutions
Introduction To Quantum Mechanics
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- Chapter 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_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_forward
- Derive 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▼ 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_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_forward
- Problem 3: Calculate the energy changes corresponding to the transitions of the hydrogen atom. Give all your answers in eV. Part (a) From n = 3 to n = 4. Part (b) From n = 2 to n = 1. Part (c) From n = 3 to n = ∞.arrow_forwarda) Calculate the energy of the emissive transition with the lowest energy possible for the Lyman series, for a mole of hydrogen atoms. Express your answer in joules/mol. b) Is this transition in the visible spectral domain? If not, in which region is it located?arrow_forwardConsider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?arrow_forward
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