Chapter 42: Nuclear Physics

Question: Using a nuclidic chart, write the symbols for (a) all stable isotopes with Z = 60, (b) all radioactive nuclides with N = 60, and (c) all nuclides with A = 60.

If the unit for atomic mass were defined so that the mass of ${\mathbf{}}^{\mathbf{1}}\mathbf{H}\mathbf{}$were exactly 1.000 000 u, what would be the mass of(a) localid="1661600852143" ${\mathbf{}}^{\mathbf{12}}\mathbf{C}\mathbf{}$(actual mass 12. 000 000 u ) localid="1661600855467" ${\mathbf{}}^{\mathbf{238}}\mathbf{U}\mathbf{}$and (b) (actual mass 238.050 785 u)?

High-mass radionuclides, which may be either alpha or beta emitters, belong to one of four decay chains, depending on whether their mass number A is of the form 4n, 4n+1, 4n+2, or 4n+3, where n is a positive integer. (a) Justify this statement and show that if a nuclide belongs to one of these families, all its decay products belong to the same family. Classify the following nuclides as to family: (b) ${\mathbf{}}^{\mathbf{235}}\mathbf{U}$(c) localid="1661601960557" ${\mathbf{}}^{\mathbf{236}}\mathbf{U}\mathbf{}$(d) ${\mathbf{}}^{\mathbf{238}}\mathbf{U}$ (e) localid="1661601429038" ${\mathbf{}}^{\mathbf{239}}\mathbf{PU}$ (f) localid="1661601438307" ${\mathbf{}}^{\mathbf{240}}\mathbf{PU}$(g) localid="1661601952668" ${\mathbf{}}^{\mathbf{245}}\mathbf{PU}$ (h) localid="1661601482780" ${\mathbf{}}^{\mathbf{246}}\mathbf{Cm}$ (i) ${\mathbf{}}^{\mathbf{249}}\mathbf{Cf}$and (j) ${\mathbf{}}^{\mathbf{249}}\mathbf{Fm}$.

Locate the nuclides displayed in Table 42-1 on the nuclidic chart of Fig. 42-5. Verify that they lie in the stability zone.

The radionuclide ${\mathbf{}}^{\mathbf{32}}\mathbf{P}$(T1/2 = 14.28 d) is often used as a tracer to follow the course of biochemical reactions involving phosphorus. (a) If the counting rate in a particular experimental setup is initially 3050 counts/s, how much time will the rate take to fall to 170 counts/s? (b) A solution containing ${\mathbf{}}^{\mathbf{32}}\mathbf{P}$is fed to the root system of an experimental tomato plant, and the ${\mathbf{}}^{\mathbf{32}}\mathbf{P}$activity in a leaf is measured 3.48 days later. By what factor must this reading be multiplied to correct for the decay that has occurred since the experiment began?

Question: At the end of World War II, Dutch authorities arrested Dutch artist Hans van Meegeren for treason because, during the war, he had sold a masterpiece painting to the Nazi Hermann Goering. The painting, Christ and His Disciples at Emmausby Dutch master Johannes Vermeer (1632–1675), had been discovered in 1937 by van Meegeren, after it had been lost for almost 300 years. Soon after the discovery, art experts proclaimed that Emmauswas possibly the best Vermeer ever seen. Selling such a Dutch national treasure to the enemy was unthinkable treason. However, shortly after being imprisoned, van Meegeren suddenly announced that he, not Vermeer, had painted Emmaus. He explained that he had carefully mimicked Vermeer's style, using a 300-year-old canvas and Vermeer’s choice of pigments; he had then signed Vermeer’s name to the work and baked the painting to give it an authentically old look.

Was van Meegeren lying to avoid a conviction of treason, hoping to be convicted of only the lesser crime of fraud? To art experts, Emmauscertainly looked like a Vermeer but, at the time of van Meegeren’s trial in 1947, there was no scientific way to answer the question. However, in 1968 Bernard Keisch of Carnegie-Mellon University was able to answer the question with newly developed techniques of radioactive analysis.

Specifically, he analyzed a small sample of white lead-bearing pigment removed from Emmaus. This pigment is refined from lead ore, in which the lead is produced by a long radioactive decay series that starts with unstable${}^{\mathbf{238}}\mathbf{U}$and ends with stable${}^{\mathbf{206}}\mathbf{PB}$.To follow the spirit of Keisch’s analysis, focus on the following abbreviated portion of that decay series, in which intermediate, relatively short-lived radionuclides have been omitted:

${}^{\mathbf{230}}\mathbf{Th}\underset{\mathbf{75}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{ky}}{\mathbf{\to }}{}^{\mathbf{226}}\mathbf{Ra}\underset{\mathbf{1}\mathbf{.}\mathbf{60}\mathbf{}\mathbf{ky}}{\mathbf{\to }}{}^{\mathbf{210}}\mathbf{Pb}\underset{\mathbf{22}\mathbf{.}\mathbf{6}\mathbf{}\mathbf{y}}{\mathbf{\to }}{}^{\mathbf{206}}\mathbf{Pb}$

The longer and more important half-lives in this portion of the decay series are indicated.

$\frac{\mathbf{d}{\mathbf{N}}_{\mathbf{210}}}{\mathbf{d}\mathbf{t}}\mathbf{=}{\mathit{\lambda }}_{\mathbf{226}}{\mathit{N}}_{\mathbf{226}}\mathbf{-}{\mathit{\lambda }}_{\mathbf{210}}{\mathit{N}}_{\mathbf{210}\mathbf{,}}$

where${\mathbf{N}}_{\mathbf{210}\mathbf{}}\mathbf{and}\mathbf{}{\mathbf{N}}_{\mathbf{226}}$are the numbers of${}^{\mathbf{210}}\mathbf{Pb}$nuclei and ${}^{\mathbf{226}}\mathbf{Ra}$nuclei in the sample and${\mathit{\lambda }}_{\mathbf{210}}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{\lambda }}_{\mathbf{226}}$are the corresponding disintegration constants. Because the decay series has been active for billions of years and because the half-life of ${}^{\mathbf{210}}\mathbf{Pb}$is much less than that of role="math" localid="1661919868408" ${}^{\mathbf{226}}\mathbf{Ra}$, the nuclides${}^{\mathbf{226}}\mathbf{Ra}\mathbf{}\mathbf{and}\mathbf{}{}^{\mathbf{210}}\mathbf{Pb}$are in equilibrium; that is, the numbers of these nuclides (and thus their concentrations) in the sample do not change. (b) What is the ratio$\frac{{\mathbf{R}}_{\mathbf{226}}}{{\mathbf{R}}_{\mathbf{210}}}$of the activities of these nuclides in the sample of lead ore? (c) What is the $\frac{{\mathbf{N}}_{\mathbf{226}}}{{\mathbf{N}}_{\mathbf{210}}}$ratioof their numbers? When lead pigment is refined from the ore, most of the radium${}^{\mathbf{226}}\mathbf{Ra}$ is eliminated. Assume that only 1.00% remains. Just after the pigment is produced, what are the ratios (d)$\frac{{\mathbf{R}}_{\mathbf{226}}}{{\mathbf{R}}_{\mathbf{210}}}$ and (e)$\frac{{\mathbf{N}}_{\mathbf{226}}}{{\mathbf{N}}_{\mathbf{210}}}$? Keisch realized that with time the ratio$\frac{{\mathbf{R}}_{\mathbf{226}}}{{\mathbf{R}}_{\mathbf{210}}}$of the pigment would gradually change from the value in freshly refined pigment back to the value in the ore, as equilibrium between the${}^{\mathbf{210}}\mathbf{Pb}$and the remaining${}^{\mathbf{226}}\mathbf{Ra}$is established in the pigment. If Emmauswere painted by Vermeer and the sample of pigment taken from it was 300 years old when examined in 1968, the ratio would be close to the answer of (b). If Emmauswere painted by van Meegeren in the 1930s and the sample were only about 30 years old, the ratio would be close to the answer of (d). Keisch found a ratio of 0.09. (f) Is Emmausa Vermeer?

From data presented in the first few paragraphs of Module 42-3, find (a) the disintegration constant $\mathit{\lambda }$and (b) the half-life of 238U

The ${\mathbf{nuclide}}^{\mathbf{14}}\mathbf{C}$contains (a) how many protons and (b) how many neutrons?

Find the disintegration energy Q for the decay of ${\mathbf{}}^{\mathbf{49}}\mathit{V}$by Kelectron capture (see Problem 54). The needed data are ${\mathbf{m}}_{\mathbf{v}}\mathbf{=}\mathbf{48}\mathbf{.}\mathbf{94852}\mathbf{}\mathbf{u}\mathbf{,}\mathbf{}{\mathbf{m}}_{\mathbf{n}}\mathbf{=}\mathbf{48}\mathbf{.}\mathbf{94787}\mathbf{u}$and .

Att = 0we begin to observe two identical radioactive nuclei that have a half-life of. At t = 1min, one of the nuclei decays. Does that event increase or decrease the chance that the second nucleus will decay in the next, or is there no effect on the second nucleus? (Are the events cause and effect, or random?)