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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…..(1)

Hence, Radius of hydrogen is,

rn=a0…..(2)

And radius of beryllium ion is given by,

rb=1312a0

rb=a03…..(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

Verify for the angular solutions ⊙(θ)φ(ϕ)of Table 7.3 that replacing ϕ with ϕ+π and replacing θ with π-θgives the same function whenis even and the negative of the function when lis odd.

A particle orbiting due to an attractive central force has angular momentum L=1.00×10-33kg.m/s What z-components of angular momentum is it possible to detect?

In Table 7.5, the pattern that develops with increasing n suggests that the number of different sets ofl,mlvalues for a given energy level n isn2. Prove this mathematically by summing the allowed values ofmlfor a givenlover the allowed values oflfor a given n.

A simplified approach to the question of how lis related to angular momentum – due to P. W. Milonni and Richard Feynman – can be stated as follows: If can take on only those values mlh, whereml=0,±1,……±l , then its square is allowed only valuesml2h2, and the average of localid="1659178449093" l2should be the sum of its allowed values divided by the number of values,2l+1 , because there really is no preferred direction in space, the averages of Lx2andLy2should be the same, and sum of all three should give the average of role="math" localid="1659178641655" L2. Given the sumrole="math" localid="1659178770040" ∑1Sn2=N(N+1)(2N+1)/6, show that these arguments, the average of L2 should be l(l+1)h2.

Verify that the solution given in equation (7.6) satisfy differential equations (7.5) as well as the required boundary conditions.
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