Open Question
A 26.00-g sample of water containing tritium, ³¹H, emits 1.50 * 10³ beta particles per second. Tritium is a weak beta emitter with a half-life of 12.3 years. What fraction of all the hydrogen in the water sample is tritium?
Ch.21 - Nuclear Chemistry
Chapter 21, Problem 86
Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits 8 * 10^-13 J of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.
Verified step by step guidance1
Step 1: Convert the radioactivity from picocuries (pCi) to disintegrations per second (dps). Use the conversion factor: 1 Curie (Ci) = 3.7 x 10^10 disintegrations per second. Since 1 pCi = 10^-12 Ci, calculate the disintegrations per second for 2 pCi.
Step 2: Calculate the total energy deposited in 1 year. First, find the number of disintegrations in 1 year by multiplying the disintegrations per second by the number of seconds in a year (365 days x 24 hours/day x 3600 seconds/hour). Then, multiply the total number of disintegrations by the energy deposited per alpha particle (8 x 10^-13 J).
Step 3: Calculate the absorbed dose in rads. The absorbed dose in rads is the energy deposited per unit mass of tissue. Use the formula: absorbed dose (rads) = (total energy deposited in joules) / (mass in kg x 0.01 J/kg).
Step 4: Convert the absorbed dose from rads to rems. Since the radiation weighting factor for alpha particles is 20, use the formula: dose in rems = dose in rads x radiation weighting factor.
Step 5: Summarize the calculations to find the number of disintegrations per second, the total energy deposited in 1 year, the absorbed dose in rads, and the dose in rems.
Related Practice
Open Question
The Sun radiates energy into space at the rate of 3.9 * 1026 J/s. (a) Calculate the rate of mass loss from the Sun in kg/s. (b) How does this mass loss arise? (c) It is estimated that the Sun contains 9 * 1056 free protons. How many protons per second are consumed in nuclear reactions in the Sun?
Open Question
The average energy released in the fission of a single uranium-235 nucleus is about 3 * 10^-11 J. If the conversion of this energy to electricity in a nuclear power plant is 40% efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces 1000 megawatts? Recall that a watt is 1 J/s.
Open Question
A 53.8-mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half-life of chlorine-36 is 3.0 * 105 yr.
Open Question
Calculate the mass of octane, C8H18, that must be burned in air to evolve the same quantity of energy as produced by the fusion of 1.0 g of hydrogen in the following fusion reaction: 4 1^1H → 4 2He + 2 0^1e. Assume that all the products of the combustion of octane are in their gas phases. Use data from Exercise 21.50, Appendix C, and the inside covers of the text. The standard enthalpy of formation of octane is -250.1 kJ/mol.
Open Question
Naturally found uranium consists of 99.274% 238U, 0.720% 235U, and 0.006% 234U. As we have seen, 235U is the isotope that can undergo a nuclear chain reaction. Most of the 235U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF6(g). (a) What is the mass of UF6 in a 30.0-L vessel of UF6 at a pressure of 695 torr at 350 K? (b) What is the mass of 235U in the sample described in part (a)? (c) Now suppose that the UF6 is diffused through a porous barrier and that the change in the ratio of 238U and 235U in the diffused gas can be described by Equation 10.23. What is the mass of 235U in a sample of the diffused gas analogous to that in part (a)? (d) After one more cycle of gaseous diffusion, what is the percentage of 235UF6 in the sample?