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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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Mathematically equation (7-22) is the same differential equation as we had for a particle in a box-the function and its second derivative are proportional. But(蠒)for m1= 0is a constant and is allowed, whereas such a constant wave function is not allowed for a particle in a box. What physics accounts for this difference?

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