Natural uranium must be processed to produce uranium enriched in 235U for weapons and power plants. The process- ing yields a large quantity of nearly pure 238U as a by-product, called “depleted uranium." Because of its high mass density, 238U is used in armor-piercing artilleryshells. (a) Find the edge dimension of a 70.0-kg cube of 238U (p = 19.1 × 10$ kg/m³). (b) The isotope 238U has a long half-life of 4.47 x 10° yr. As soon as one nucleus decays, a relatively rapid series of 14 steps begins that together constitute the net reaction 238U → 92 8(He) + 6(_'e) + 206Pb + 6v + Qnet Find the net decay energy. (Refer to Table 43.2.) (c) Argue that a radioactive sample with decay rate Rand decay energy Q has power output P = QR. (d) Consider an artillery shell with a jacket of 70.0 kg of 258U. Find its power output due to the radioactivity of the uranium and its daughters. Assume the shell is old enough that the daughters have reached steady-state amounts. Express the power in joules per year. (e) What If? A l7-year-old soldier of mass 70.0 kg works in an arsenal where many such artillery shells are stored. Assume his radiation exposure is limited to 5.00 rem per year. Find the rate in joules per year at which he can absorb energy of radiation. Assume an average RBE factor of 1.10.

Natural uranium must be processed to produce uranium enriched in 235U for weapons and power plants. The process- ing yields a large quantity of nearly pure 238U as a by-product, called “depleted uranium." Because of its high mass density, 238U is used in armor-piercing artilleryshells. (a) Find the edge dimension of a 70.0-kg cube of 238U (p = 19.1 × 10$ kg/m³). (b) The isotope 238U has a long half-life of 4.47 x 10° yr. As soon as one nucleus decays, a relatively rapid series of 14 steps begins that together constitute the net reaction 238U → 92 8(He) + 6(_'e) + 206Pb + 6v + Qnet Find the net decay energy. (Refer to Table 43.2.) (c) Argue that a radioactive sample with decay rate Rand decay energy Q has power output P = QR. (d) Consider an artillery shell with a jacket of 70.0 kg of 258U. Find its power output due to the radioactivity of the uranium and its daughters. Assume the shell is old enough that the daughters have reached steady-state amounts. Express the power in joules per year. (e) What If? A l7-year-old soldier of mass 70.0 kg works in an arsenal where many such artillery shells are stored. Assume his radiation exposure is limited to 5.00 rem per year. Find the rate in joules per year at which he can absorb energy of radiation. Assume an average RBE factor of 1.10.