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Chapter 36: Problem 2

A friend who hasn't studied physics asks you the size of a hydrogen atom. How do you answer?

Short Answer

Expert verified
A hydrogen atom is incredibly small, with a size of about 53 picometers (one trillionth of a meter). For perspective, if a hydrogen atom were the size of a one-meter ball, a human hair in the same scale would be around 1 kilometer thick.

Step by step solution

01

Simplify the concept

Firstly, consider that matter is mostly empty space. Even a tiny hydrogen atom, which is the smallest atom, consists primarily of empty space. The atom itself is roughly a trillionth of a centimeter in size.
02

Provide a standard measurement

The size of a hydrogen atom is generally measured in terms of its atomic radius. For a hydrogen atom, this is around 53 picometers (1 picometer = \(1 \times 10^{-12}\) meters). This is often considered the 'size' of the atom.
03

Relate to everyday objects

To put this size into perspective, if a hydrogen atom was magnified until it was one meter in diameter, a human hair would be approximately 1 kilometer in diameter.

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Most popular questions from this chapter

Repeat Exercise 25 for the case where you know only that the principal quantum number is \(3 ;\) that is, \(l\) might have any of its possible values.

Determine the electronic configuration of copper.

Suppose you put five electrons into an infinite square well of width \(L\). Find an expression for the minimum energy of this system, consistent with the exclusion principle.

With sufficient energy, it's possible to eject an electron from an inner atomic orbital. A higher-energy electron will then drop into the unoccupied state, emitting a photon with energy equal to the difference between the two levels. For inner-shell electrons, photon energies are in the keV range, putting them in the X-ray region of the spectrum. These characteristic X rays are labeled with the letter indicating the shell to which the electron drops, followed by a Greek letter indicating the higher level from which it drops; thus \(K \alpha\) designates a transition from the \(L\) shell to the \(K\) shell. Characteristic X rays provide scientists and physicians with an important diagnostic tool. Environmental scientists bombard pollution samples with high- energy electrons, knocking out inner-shell electrons and thus producing X-ray spectra that help identify contaminants (Fig. \(36.20 a\) ). Geologists do the same with rocks. Medical radiologists reverse the process, exploiting the fact that X rays cause inner-shell transitions as well as complete ejection of inner-shell electrons. In particular, radiologists use the element barium in this way to produce high-contrast X-ray images of the intestinal tract \((\text { Fig. } 36.20 b)\)(GRAPH CANNOT COPY) (a) An \(\mathrm{X}\) -ray spectrum from air pollutants trapped on a filter. The labeled peaks show the presence of lead (Pb) and arsenic (As), as evidenced by \(K \alpha, K \beta, L \alpha,\) and \(L \beta\) characteristic X rays. (b) \(\mathrm{X}\) -ray of an intestinal tract, made by coating the intestinal wall with X-ray-opaque barium Elements \(A\) and \(B\) have atomic numbers \(Z_{A}\) and \(Z_{B}=2 Z_{A} .\) How do you expect element \(B^{\prime}\) s \(K \alpha\) X-ray energy to compare with that of element \(A\) ? a. \(B^{\prime}\) s \(K \alpha\) energy should be about one-fourth that of \(A\) b. \(B\) 's \(K \alpha\) energy should be about half that of \(A\) c. \(B^{\prime}\) s \(K \alpha\) energy should be about twice that of \(A\) d. \(B^{\prime}\) s \(K \alpha\) energy should be about four times that of \(A\)

A selection rule for the infinite square well allows only those transitions in which \(n\) changes by an odd number. Suppose an infinite square well of width 0.200 nm contains an electron in the \(n=4\) state. (a) Draw an energy-level diagram showing all allowed transitions that could occur as this electron drops toward the ground state, including transitions from lower levels that could be reached from \(n=4 .\) (b) Find all the possible photon energies emitted in these transitions.
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