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Chapter 8: Q11CQ (page 338)

Question: The “radius of an atom” is a debatable quantity. Why?

Short Answer

Expert verified

Answer

Half the distance between the nuclei of identical neighboring atoms in the solid form of an element.

Step by step solution

01

Radius of the atom

The radius of an atom is about 0.1 nm (1×10-10m)

The wave function for the electrons in atoms does not have an abrupt change to zero at some specific radius and beyond Instead, the wave function.

02

Explanation.

And therefore the probability density for finding an electron at a given distance from the nucleus falls off exponentially with a tail that extends to infinite distance once the distance is large enough. It is therefore somewhat ambiguous to decide at what distance the probability of finding an electron has become small enough to regard that location as outside the radius of the atom.

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Most popular questions from this chapter

Verify that the normalization constant given in Example 8.2is correct for both symmetric and antisymmetric states and is independent ofnand n'?

Imagine two indistinguishable particles that share an attraction. All other things being equal, would you expect their multiparticle spatial state to be symmetric, ant symmetric, or neither? Explain.

The radius of cesium is roughly0.26nm.

(a) From this estimate the effective charge its valence electron orbits

(b) Given the nature of the electron's orbit. is this effective nuclearcharge reasonable?

(c) Compare this effective Zwith that obtained for sodium in Example 8.3. Are the values at odds with the evidence given in Figure8.16that it takes less energy to remove an electron from cesium than from sodium? Explain.

A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets {sT,LT}of their total spin and total orbital angular momentum? Ignore possibilities in which sT is 2 or higher.

Whether adding spins to get total spin, spin and orbit to get total angular momentum, or total angular momenta to get a "grand total" angular momentum, addition rules are always the same: Given J1=ℏj1(j1+1)andJ2=ℏj2(j2+1) . Where is an angular momentum (orbital. spin. or total) and a quantum number. the total isJT=ℏjT(jT+1) , where jTmay take on any value between |j1-j2|and j1+j2in integral steps: and for each value ofJΓJTz=mπf . where mπmay take on any of2jr+I possible values in integral steps from-jT for +jTSince separately there would be 2j1+1possible values form11 and2j2+ I formρ2 . the total number of stales should be(2j1+1)(2j2+1) . Prove it: that is, show that the sum of the2jT+1 values formit over all the allowed values forj7 is (2j1+1)(2j2+1). (Note: Here we prove in general what we verified in Example 8.5for the specialcase j1=3,j2=12.)
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