Pearson eText for College Physics: Explore and Apply -- Instant Access (Pearson+)
2nd Edition
ISBN: 9780137443000
Author: Eugenia Etkina, Gorazd Planinsic
Publisher: PEARSON+
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Chapter 28, Problem 47P
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3.
eV.
Consider an atom of triply ionized beryllium Be³+ with an energy of -9.704
(a) List all the possible states, excluding spin, of the hydrogen atom with this energy.
(b) What is the degree of degeneracy?
(c) What is the maximum possible angular momentum L (as a multiple of ħ)?
For what energy levels in the hydrogen atom will we
not find l
2 states?
=
A hydrogen atom is in the 4d state.
a) What is the magnitude of the orbital angular momentum?
b) Calculate the possible values of the total angular momentum quantum number.
c) Calculate the magnitude of the total angular momentum for each value in (b).
Chapter 28 Solutions
Pearson eText for College Physics: Explore and Apply -- Instant Access (Pearson+)
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- What are the possible values of m for an electron in the n = 4 state?arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.arrow_forwardHow many electrons can occupy the system with l=0, l=2 and l=4. What is number of possible orientations of the orbital angular momentum with l=4? What is the smallest z-component of the orbital angular momentum?arrow_forward
- The energy levels of hydrogen atom (including fine structure term ) takes the following form a? 1+ 13.6ev п 3 E j+1/2 4 n° Write down the energy levels for the state n=3arrow_forwardWhich of the following sets of quantum numbers can be used to describe the 2 electrons in the He atom? For the possible sets, write the electron configuration and identify if it is a ground state or excited state configuration. i) n = 2,1 = 0, mį = 0, mş = 1/2 and n = 1, 1 = 0, m = 0, mş = 1/2 ii) n = 2,1= 0, mi = 0, ms = 1/2 and n = 2,1= 0, mi = 0, ms = 1/2 iii) n = 2,1= 1, mị = 0, mş = 1/2 and n = 2,1= 0, mį = 0, ms = 1/2 iv) n = 2,1= 0, mį = 0, ms =- 1/2 and n = 2,1= 0, m¡ = 0, ms = 1/2 v) n = 1,1= 0, mį = 0, mş = 2 and n = 1,1 = 0, mį = 0, mş = -2 %3D %3D %3D %3Darrow_forwardIn another universe, the electron is a spin@3/2 rather than a spin@1/2 particle, but all other physics are the same as in our universe. In this universe what is the ground-state electron configuration of sodium?arrow_forward
- Consider the atom having the electron configuration 1s2 2s2 2p6 3s2. Assume that the z components of both the orbital abd spin angular momenta of the electron in the 3p subshell are positive. What are the quantum numbers that describe the state of this electron. n=3 l=1 m=-1 s=1/2n=3 l=1 m=2 s=1/2n=3 l=2 m=1 s=1/2n=3 l=1 m=1 s=1/2n=3 l=2 m=2 s=-1/2 Can we say which one is correct?arrow_forwardc. n= 2, 1 = 0. 2. Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 3, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forward
- A cubical box of widths L, = Ly =L; = L = 1.5 nm contains four electrons. What is the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin. E= iarrow_forwardCalculate the energy of an electron in the n = 3 state in a hydrogen atom. a) 2.42 × 10-19 J d) −7.27 × 10-19 J b) −2.42 × 10-19 J e) −6.54 × 10-18 J c) 7.27 × 10-19 Jarrow_forwardConsider the atom having the electron configuration 1s2 2s2 2p6 3s2 3p1. Which of the following statements are correct? Tick all that apply, say the correct options. The atom has no electrons in tje energy level n=3 ?the atom has only electron in the state n=3 I=2 ?the atom has six electrons in the state n=2 I=1 ?The atom has three electrons in the energy level for which n=3 ?The atom has electrons in states n=2 and n=3 ?arrow_forward
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