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Chapter 5: Q9P (page 214)

(a) Suppose you put both electrons in a helium atom into the n=2state;

what would the energy of the emitted electron be?

(b) Describe (quantitatively) the spectrum of the helium ion,He+.

Short Answer

Expert verified

(a)The energy of the emitted electron is 2E1-4E1=-2E1=27.2eV

(b)Helium has one electron and it鈥檚 a hydrogenise ion with z=2 so the spectrum

is1/位=4R(1/nf2-1/ni2)

Step by step solution

01

(a) The energy of the emitted electron

The energy of each electron isE=Z2E1/n2=4E1/4=E1=E1=-13.6eV,

so the total initial energy is2脳-13.6eV=-27.2eV.

One electron drops to the ground state Z2E1/1=4E1, so the other is left

with 2E1-4E1=-2E1=27.2eV.

02

(b) The spectrum of the helium ion

(b) He+has one electron; it鈥檚 a hydrogenise ion with Z = 2, so the spectrum

is 1/位=4R1/nf2-1/ni2, where R is the hydrogen Rydberg constant, and ni,nfare the

initial and final quantum numbers (1, 2, 3, . . . ).

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Most popular questions from this chapter

Imagine two noninteracting particles, each of mass m, in the infinite square well. If one is in the state蠄n(Equation 2.28 ), and the other in state 蠄1(l鈮�n), calculate localid="1658214464999" (x1-x2)2, assuming (a) they are distinguishable particles, (b) they are identical bosons, and (c) they are identical fermions.

Calculate the Fermi energy for noninteracting electrons in a two-dimensional infinite square well. Let 蟽 be the number of free electrons per unit area.

Suppose you had three particles, one in state蠄a(x), one in state蠄b(x), and one in state蠄c(x). Assuming 蠄a,蠄b, and蠄c are orthonormal, construct the three-particle states (analogous to Equations 5.15,5.16, and 5.17) representing

(a) distinguishable particles,

(b) identical bosons, and

(c) identical fermions.

Keep in mind that (b) must be completely symmetric, under interchange of any pair of particles, and (c) must be completely antisymmetric, in the same sense. Comment: There's a cute trick for constructing completely antisymmetric wave functions: Form the Slater determinant, whose first row is蠄a(x1),蠄b(x1),蠄c(x1) , etc., whese second row is蠄a(x2),蠄b(x2),蠄c(x2) , etc., and so on (this device works for any number of particles).

Discuss (qualitatively) the energy level scheme for helium if (a) electrons were identical bosons, and (b) if electrons were distinguishable particles (but with the same mass and charge). Pretend these 鈥渆lectrons鈥� still have spin 1/2, so the spin configurations are the singlet and the triplet.

(a) Using Equations 5.59 and 5.63, show that the wave function for a particle in the periodic delta-function potential can be written in the form

蠄(X)=C[sinkx+e-ikasina-x]0鈮�x鈮�a

(b) There is an exception; At the top of a band where z is an integer multiple of蟺yiels蠄(x)=0 yields .

Find the correct wave function for the case. Note what happens to蠄each delta function.
See all solutions

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