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To obtain the most precise value of BE from the equation BE= ZM 1 H + Nm n c 2 m A X c 2 size 12{"BE=" left lbrace left [ ital "ZM" left ("" lSup { size 8{1} } H right )+ ital "Nm" rSub { size 8{n} } right ]-m left ("" lSup { size 8{A} } X right ) right rbrace c rSup { size 8{2} } } {} , we should take into account the binding energy of the electrons in the neutral atoms. Will doing this produce a larger or smaller value for BE? Why is this effect usually negligible?

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How does the finite range of the nuclear force relate to the fact that BE / A size 12{ {"BE"} slash {A} } {} is greatest for A size 12{A} {} near 60?

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Problems&Exercises

Data from the appendices and the periodic table may be needed for these problems.

An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14 C size 12{"" lSup { size 8{"14"} } C} {} . Estimate the minimum age of the charcoal, noting that 2 10 = 1024 size 12{2 rSup { size 8{"10"} } ="1024"} {} .

57,300 y

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A 60 Co size 12{"" lSup { size 8{"60"} } "Co"} {} source is labeled 4.00 mCi, but its present activity is found to be 1 . 85 × 10 7 size 12{1 "." "85" times "10" rSup { size 8{7} } } {} Bq. (a) What is the present activity in mCi? (b) How long ago did it actually have a 4.00-mCi activity?

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(a) Calculate the activity R size 12{R} {} in curies of 1.00 g of 226 Ra size 12{"" lSup { size 8{"226"} } "Ra"} {} . (b) Discuss why your answer is not exactly 1.00 Ci, given that the curie was originally supposed to be exactly the activity of a gram of radium.

(a) 0.988 Ci

(b) The half-life of 226 Ra size 12{"" lSup { size 8{"226"} } "Ra"} {} is now better known.

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Show that the activity of the 14 C size 12{"" lSup { size 8{"14"} } C} {} in 1.00 g of 12 C size 12{"" lSup { size 8{"12"} } C} {} found in living tissue is 0.250 Bq.

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Mantles for gas lanterns contain thorium, because it forms an oxide that can survive being heated to incandescence for long periods of time. Natural thorium is almost 100% 232 Th size 12{"" lSup { size 8{"232"} } "Th"} {} , with a half-life of 1 . 405 × 10 10 y size 12{1 "." "405" times "10" rSup { size 8{"10"} } } {} . If an average lantern mantle contains 300 mg of thorium, what is its activity?

1.22 × 10 3 Bq

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Cow’s milk produced near nuclear reactors can be tested for as little as 1.00 pCi of 131 I size 12{"" lSup { size 8{"131"} } I} {} per liter, to check for possible reactor leakage. What mass of 131 I size 12{"" lSup { size 8{"131"} } I} {} has this activity?

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(a) Natural potassium contains 40 K , which has a half-life of 1 . 277 × 10 9 size 12{1 "." "277" times "10" rSup { size 8{9} } } {} y. What mass of 40 K size 12{"" lSup { size 8{"40"} } K} {} in a person would have a decay rate of 4140 Bq? (b) What is the fraction of 40 K size 12{"" lSup { size 8{"40"} } K} {} in natural potassium, given that the person has 140 g in his body? (These numbers are typical for a 70-kg adult.)

(a) 16.0 mg

(b) 0.0114%

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There is more than one isotope of natural uranium. If a researcher isolates 1.00 mg of the relatively scarce 235 U size 12{"" lSup { size 8{"235"} } U} {} and finds this mass to have an activity of 80.0 Bq, what is its half-life in years?

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50 V has one of the longest known radioactive half-lives. In a difficult experiment, a researcher found that the activity of 1.00 kg of 50 V is 1.75 Bq. What is the half-life in years?

1.48 × 10 17 y size 12{ {underline {1 "." "48" times "10" rSup { size 8{"17"} } y}} } {}

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You can sometimes find deep red crystal vases in antique stores, called uranium glass because their color was produced by doping the glass with uranium. Look up the natural isotopes of uranium and their half-lives, and calculate the activity of such a vase assuming it has 2.00 g of uranium in it. Neglect the activity of any daughter nuclides.

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A tree falls in a forest. How many years must pass before the 14 C size 12{"" lSup { size 8{"14"} } C} {} activity in 1.00 g of the tree’s carbon drops to 1.00 decay per hour?

5.6 × 10 4 y size 12{ {underline {5 "." 6 times "10" rSup { size 8{4} } y}} } {}

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What fraction of the 40 K size 12{"" lSup { size 8{"40"} } K} {} that was on Earth when it formed 4 . 5 × 10 9 years ago is left today?

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A 5000-Ci 60 Co source used for cancer therapy is considered too weak to be useful when its activity falls to 3500 Ci. How long after its manufacture does this happen?

2.71 y

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Practice Key Terms 8

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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