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Chapter 7: Q68E (page 283)

Roughly, how does the size of a triply ionized beryllium ion compare with hydrogen?

Short Answer

Expert verified

The Triple ionized beryllium ion is roughly 1/3rd as compared to the radius of the hydrogen atom.

Step by step solution

01

A concept:

Ionization decreases the size of the object as the nucleus has to hold fewer electrons, hence, ionization energy increases and it becomes more difficult to remove electrons.

02

Radii of triply ionized beryllium ion and hydrogen:

From eq. (7-42), you get,

Radius of hydrogen like atoms is,

rn=1Zn2a0鈥�..(1)

Hence, Radius of hydrogen is,

rn=a0鈥�..(2)

And radius of beryllium ion is given by,

rb=1312a0

rb=a03鈥�..(3)

03

Conclusion:

From equation (2) and (3) into equation (1), and you get the following.

The Triply ionized beryllium ion is roughly 1/3rd as compared to the radius of the hydrogen atom.

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Most popular questions from this chapter

Exercise 81 obtained formulas for hydrogen like atoms in which the nucleus is not assumed infinite, as in the chapter, but is of mass m1, whilem2is the mass of the orbiting negative charge. In positronium, an electron orbits a single positive charge, as in hydrogen, but one whose mass is the same as that of the electron -- a positron. Obtain numerical values of the ground state energy and 鈥淏ohr radius鈥� of positronium.

Question: Consider an electron in the ground state of a hydrogen atom. (a) Calculate the expectation value of its potential energy. (b) What is the expectation value of its kinetic energy? (Hint: What is the expectation value of the total energy?)

A mathematical solution of the azimuthal equation (7-22) is 桅(蠁)=Ae-顿蠁+Be-顿蠁 , which applies when D is negative, (a) Show that this simply cannot meet itself smoothly when it finishes a round trip about the z-axis. The simplest approach is to consider 蠁=0 and 蠁=2蟺. (b) If D were 0, equation (7-22) would say simply that the second derivative 桅(蠁)of is 0. Argue than this too leads to physically unacceptable solution, except in the special case of 桅(蠁) being constant, which is covered by the ml=0 , case of solutions (7-24).

An electron confinedtoa cubic 3D infinite well 1 nu on aside.

  1. What are thethree lowest differentenergies?
  2. To how many different states do these three energies correspond?

Consider a cubic 3D infinite well.

(a) How many different wave functions have the same energy as the one for which (nx,ny,nz)=(5,1,1)?

(b) Into how many different energy levels would this level split if the length of one side were increased by 5% ?

(c) Make a scale diagram, similar to Figure 3, illustrating the energy splitting of the previously degenerate wave functions.

(d) Is there any degeneracy left? If so, how might it be 鈥渄estroyed鈥�?
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