Ignoring the fine structure splitting, hyperfine structure splitting, etc., such that energy levels depend only on the principal quantum number n, how many distinct states of singly-ionized helium (Z = 2) have energy E= -13.6 eV? Write out all the quantum numbers (n, l, m, m,) describing each distinct state. (Recall that the ground state energy of hydrogen is E₁ = -13.6 eV, and singly-ionized helium may be treated as a hydrogen-like atom.)

Ignoring the fine structure splitting, hyperfine structure splitting, etc., such that energy levels depend only on the principal quantum number n, how many distinct states of singly-ionized helium (Z = 2) have energy E= -13.6 eV? Write out all the quantum numbers (n, l, m, m,) describing each distinct state. (Recall that the ground state energy of hydrogen is E₁ = -13.6 eV, and singly-ionized helium may be treated as a hydrogen-like atom.)

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter31: Radioactivity And Nuclear Physics

Section: Chapter Questions

Problem 3PE: (a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is...

See similar textbooks

Similar questions

1. Thermal equilibration: radiative and nonradiative contributions. A collection of two-level atoms in a crystal is coupled both to the electromagnetic surroundings with radiative decay rate Yrad and to the crystal-lattice surroundings with decay rate Ynr. Suppose the electromagnetic surroundings are somehow held at a fixed temperature Trad which is different from the fixed temperature Tür of the crystal lattice. Derive a formula for the steady-state equilibrium value of the Boltzmann temperature Ta for the level populations of the two-level atoms in this case, as a function of the two surrounding temperatures Trad and Thr, the normalized energy gap ħw/k, and the ratio Yrad/Ynr.
C. For a particle of mass 9.10938356×10-31 kg scooting back and forth on a wire of length 13×10-10 m, compute it's energy in the n = 9 state. Use: π = 3.14159265359 and h = 1.0545718×10-34 Js. Eg J. D. What is the rule for the number of nodes for a particle-in-a-box state as a function of its quantum number? Number of nodes = On ΟΙ O n-1 On--1
a) How many ways are there to arrange 3 quanta among 4 atoms in a solid? b) . the ground state energy. What is the Boltzmann factor for this excited state? >At room temperature, the fourth excited state of a microscopic oscillator is o.6 eV above
2. Consider an ideal fermionic gas in one-dimension with N electrons in a volume V. Calculate the wavevector at the Fermi level (kF) also the total energy of the system (Etotal) in terms of the number density (n).
Problem 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.
4. Consider the states with l= 4 and s= 1/2. %3D (a) For the state with the largest possible j, and largest possible m,, calculate the angle between Land S. (b) For this same state, calculate the angle between 4, and ..
Pr. 5. Calculate the force between the two atoms in the diatomic hydrogen molecule that has the following potential: V(x)=(x-xo)²-Vo. Where Vo is the binding energy and ro. 6 are constant parameters.
5. Diatomic chain. Consider the normal modes of a linear chain in which the force constants between nearest-neighbor atoms are alternately C and 10C. Let the masses be equal, and let the nearest-neighbor separation be a/2. Find w(K) at K = 0 and K T/a. Sketch in the dispersion relation by eye. This problem simu- lates a crystal of diatomic molecules such as H₂.
1. Cannot be! Imagine a certain kind of particle, such that each single-particle state can be occupied by at most M particles, with M > 1. For M = 1 and M = ∞, we recover the usual fermion and boson cases. We will focus on the case when the particles do not interact with each other, and the single particle quantum states i have energies e¿. Assume that the system is in equilibrium at temperature T and chemical potential μ. (a) (b) (c) above. Calculate the appropriate partition function for the system in the conditions discussed Compute, as a function of temperature and chemical potential, the average occupation number (n) for state i, and find simplified expressions in the low and high temperature limits. For M1, does the system have the analog of a Fermi energy, i.e. an energy at which the occupation number is discontinuous at T = 0?
1. Refer to the Table below that lists the first few spherical harmonics YM. Suppose we subject a linear rigid molecule to z-polarized microwave radiation. Show explicitly that the Y→ Yº rotational transition is allowed while the Y→ Y₂ transition is not allowed. TABLE 6.3 The first few spherical harmonics. YOU 1 (4x)¹/2 3 Y₂¹ Y₂² 1/2 Y = 87 1/2 x² = (15) (3 cos²0-1) 1/2 = sin Be 15 87 15 327 sin cos le-¹ 1/2 sin²Ge-24 Y₁ = Y₁¹ = 3 87 15 87 Y₂ = Y² = (3 15 1/2 32π cos 9 1/2 1/2 sin gel sin cos e 1/2 sin² 0e²
1. Tight-binding approximation Consider a wave function (x) in an atom. When the atoms form a solid (lattice constant a), we assume the wave function (x) = Σeiknap(x-na). (1) where the atomic wave function is copied to places na (with integer n) multiplied by the phase factor eina. Calculate the energy expectation value in state (1) using where the definitions Ek and the approximations n h² d² H = +U(x). (3) 2m dr² The denominator of (2) takes into account that (1) is not normalized. In the calculation use the normalization [ ø*(x)ø(x)dx = 1, S*(x) Hy(x) dx &*(x)(x) dx' [(x ± [ ¢*(x)Hø(x)dx = =-α o* (x±a) Ho(x) dx = -3 (2) [ø*(x ±na)Hø(x)dx = 0, n ≥2 [o¹(x ± *(x±na)o(x)dx=0, n ≥ 1. (4) (5) (6) [Hint: calculate the numerator and the denominator of (2) separately. Write both in the double-sum form Σn' En An'n and calculate all An'n making use of the periodicity of the lattice potential U(r). Assume that the number of atoms N in the chain is large, which allows you to neglect all possible…
Which one of the following statements about the exchange energy of the few lowest excited states of helium, in which the two electrons are in different subshells, is incorrect? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. b с d e In the absence of the exchange energy, the degeneracy between 1s¹2s¹ and 1s¹2p¹ configurations would only be lifted by relativistic corrections. For a given configuration and L the exchange energy favours (ie the energy is lower for) S-1 compared with S=0 O For a given configuration and L the exchange energy favours states that are spatially anti-symmetric The exchange energy gives larger shifts in the levels than relativistic corrections L, S remain good quantum numbers in the presence of the exchange energy