Problems B
409
The actual mole weights involved are ?H = 3.01710 g; fH = 2.01470 g;
|He = 4.00386 g; Jn = 1.00897 g.
(b) How many tons of carbon would have to be burned to give as much energy
as 1 Ib of hydrogen consumed by this reaction? (Carbon gives 94.1 kcal/
mole when burned to CO 2 .)
16. Radioactive sulfur has been used as a tracer in the study of the action of sulfur
as an insecticide for red spider (a citrus-fruit pest). If 10.0 mg of ifS are
absorbed by an orange, how much will remain after 6.00 months in storage?
17. A pure sample of a radioactive compound is found to have 1555 cpm at 3:30
P.M., and 960 cpm at 4:00 P.M. the same day. What is the half-life of this
isotope?
18. If you seal a 100 g sample of very pure
2
|oTh in a container for safekeeping,
and if in the distant future a scientist dissolves it and finds it to contain 0.600 g
of
2 g|Pb, how many years have elapsed since you sealed the sample? (Lead is
the stable endproduct of the radioactive decay of thorium.)
19. Willard Libby and colleagues have shown that a very small amount of the CO 2
in the air is radioactive, as explained in Problem 9. Acacia wood from the
ancient Egyptian tomb of Zoser and Sakkara has an activity of 7.62 cpm/gram
of carbon. Estimate the age of this wood (and presumably the age of the
tomb).
20. If a sample of rock contains 2.00 mg of helium for each 100 mg of
2 lc,Th,
calculate the minimal age of this thorium deposit. (Six a particles are produced as thorium disintegrates to a stable isotope of lead. Assume that none of
the helium escaped from the rock.)
21. How many grams of
2
|oTh will disintegrate in 1.00 yr if, at the outset, you have
a 1.00 g sample?
22. The positrons produced in the Bethe cycle (the production of solar energy)
react with electrons to produce y radiation. This "annihilation" reaction is
(a) Assuming that the mass of both _fe and ?e is iAi that of a proton, calculate
the energy produced in the annihilation of a single electron by a single
positron. The gram-atomic weight of [H is 1.00813 g.
(b) If a single y ray is produced by this annihilation, calculate its wavelength
from the fundamental equation E = hv, where
E = energy of the quantum of y radiation, in ergs;
h = Planck's constant = 6.626 x 10~
27 erg x sec;
v = frequency of the radiation, in sec"
1 .
[The fundamental relation between wavelength (\), velocity (c), and frequency (r) is X = civ.]
23. Two nongaseous isotopes, A and B, are involved in the same radioactive
series, which (over the past eons) has established radioactive equilibrium. The
half-life of A is 10
6 yrs, and that of B is only 1 yr. What would be the relative
409
The actual mole weights involved are ?H = 3.01710 g; fH = 2.01470 g;
|He = 4.00386 g; Jn = 1.00897 g.
(b) How many tons of carbon would have to be burned to give as much energy
as 1 Ib of hydrogen consumed by this reaction? (Carbon gives 94.1 kcal/
mole when burned to CO 2 .)
16. Radioactive sulfur has been used as a tracer in the study of the action of sulfur
as an insecticide for red spider (a citrus-fruit pest). If 10.0 mg of ifS are
absorbed by an orange, how much will remain after 6.00 months in storage?
17. A pure sample of a radioactive compound is found to have 1555 cpm at 3:30
P.M., and 960 cpm at 4:00 P.M. the same day. What is the half-life of this
isotope?
18. If you seal a 100 g sample of very pure
2
|oTh in a container for safekeeping,
and if in the distant future a scientist dissolves it and finds it to contain 0.600 g
of
2 g|Pb, how many years have elapsed since you sealed the sample? (Lead is
the stable endproduct of the radioactive decay of thorium.)
19. Willard Libby and colleagues have shown that a very small amount of the CO 2
in the air is radioactive, as explained in Problem 9. Acacia wood from the
ancient Egyptian tomb of Zoser and Sakkara has an activity of 7.62 cpm/gram
of carbon. Estimate the age of this wood (and presumably the age of the
tomb).
20. If a sample of rock contains 2.00 mg of helium for each 100 mg of
2 lc,Th,
calculate the minimal age of this thorium deposit. (Six a particles are produced as thorium disintegrates to a stable isotope of lead. Assume that none of
the helium escaped from the rock.)
21. How many grams of
2
|oTh will disintegrate in 1.00 yr if, at the outset, you have
a 1.00 g sample?
22. The positrons produced in the Bethe cycle (the production of solar energy)
react with electrons to produce y radiation. This "annihilation" reaction is
(a) Assuming that the mass of both _fe and ?e is iAi that of a proton, calculate
the energy produced in the annihilation of a single electron by a single
positron. The gram-atomic weight of [H is 1.00813 g.
(b) If a single y ray is produced by this annihilation, calculate its wavelength
from the fundamental equation E = hv, where
E = energy of the quantum of y radiation, in ergs;
h = Planck's constant = 6.626 x 10~
27 erg x sec;
v = frequency of the radiation, in sec"
1 .
[The fundamental relation between wavelength (\), velocity (c), and frequency (r) is X = civ.]
23. Two nongaseous isotopes, A and B, are involved in the same radioactive
series, which (over the past eons) has established radioactive equilibrium. The
half-life of A is 10
6 yrs, and that of B is only 1 yr. What would be the relative