Exam 31: Nuclear Energy; Effects and Uses of Radiation

Consider the fusion reaction: ${ } _ { 1 } ^ { 2 } \mathrm { H } + { } _ { 1 } ^ { 2 } \mathrm { H } + { } _ { 1 } ^ { 2 } \mathrm { H } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 1 } ^ { 1 } \mathrm { H } + { } _ { 0 } ^ { 1 } \mathrm { n }$ The know atomic masses are ${ } _ { 1 } ^ { 2 } \mathrm { H } : \quad 2.01410 \mathrm { u }$ ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.00260 \mathrm { u }$ ${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.00783 \mathrm { u }$ ${ } _ { 0 } ^ { 1 } \mathrm { n } : \quad 1.008665 \mathrm { u }$ where $1 \mathrm { u } = 1.6605 \times 10 ^{- 27} \mathrm {~kg}$ . What mass of deuterium fuel, ${ } _ { 1 } ^ { 2 } \mathrm { H }$ , is used up in producing $5.6 \times 10^{15} \mathrm {~J}$ of energy by this reaction?

The maximum permissible workday dose for occupational exposure to radiation is $11 \mathrm { mrem }$ . A 77-kg laboratory technician absorbs $2.3 \mathrm {~mJ}$ of $0.5 - \mathrm { MeV }$ gamma rays in a work day. The relative biological effectiveness (RBE) for gamma rays is $1.00$ . What is the number of gamma-ray photons absorbed by the technician in a workday?

An electron and a positron, both essentially at rest, annihilate each other, emitting two identical photons in the process. What is the wavelength of these photons? The mass of an electron or positron is $9.11 \times 10 ^ { - 31 } \mathrm {~kg}$ . $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

When 235U undergoes fission, the average energy per fission event is $200 \mathrm { MeV }$ . How much energy is released in the total fission of $2.0 \mathrm {~g}$ of $235 \mathrm { U }$ ? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , m _ { \text {neutron } } \approx m _ { \text {proton } } = 1.67 \times \right.$ 10-27 kg)

The equation shows a fission reaction: ${ } _ { 92 } ^ { 235 } \mathrm { U } + { } _ { 0 } ^ { 1 } \mathrm { n } \rightarrow { } _ { 41 } ^ { 99 } \mathrm { Nb } + \mathrm { X } + 4 { } _ { 0 } ^ { 1 } \mathrm { n }$ What is the missing term $X$ in the equation?

Consider the nuclear reaction ${ } _ { 7 } ^ { 14 } \mathrm {~N} + { } _ { 2 } ^ { 4 } \mathrm { He } \rightarrow { } _ { 8 } ^ { 17 } \mathrm { O } + { } _ { 1 } ^ { 1 } \mathrm { H }$ . The known atomic masses are ${ } _ { 7 } ^ { 14 } \mathrm {~N} : \quad 14.003074 \mathrm { u }$ ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ ${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.007825 \mathrm { u }$ ${ } _ { 8 } ^ { 17 } \mathrm { O } : \quad 16.999131 \mathrm { u }$ What is the $Q$ -value (or reaction energy) of this reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

Consider the nuclear reaction ${ } _ { 7 } ^ { 14 } \mathrm {~N} + { } _ { 2 } ^ { 4 } \mathrm { He } \rightarrow { } _ { 8 } ^ { 17 } \mathrm { O } + { } _ { 1 } ^ { 1 } \mathrm { H }$ . The known atomic masses are ${ } _ { 7 } ^ { 14 } \mathrm {~N} : \quad 14.003074 \mathrm { u }$ ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ ${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.007825 \mathrm { u }$ ${ } _ { 8 } ^ { 17 } \mathrm { O } : \quad 16.999131 \mathrm { u }$ What is the Q-value (or reaction energy) of this reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } \right)$

The chief hazard of radiation damage to living cells is

In the nuclear reaction ${ } _ { 1 } ^ { 3 } \mathrm { H } + { } _ { 1 } ^ { 3 } \mathrm { H } \rightarrow \mathrm { X } + { } _ { 2 } ^ { 4 } \mathrm { He }$ , what is $\mathrm { X }$ ?

When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions. One such reaction is ${ } _ { 92 } ^ { 235 } U + { } _ { 0 } ^ { 1 } n \rightarrow { } _ { 54 } ^ { 140 } \mathrm { Xe } + { } _ { 38 } ^ { 94 } \mathrm { Sr } + 2 { } _ { 0 } ^ { 1 } \mathrm { n }$ The following mass values are known: ${ } _ { 54 } ^ { 140 }$ Xe: $\quad 139.921620 \mathrm { u }$ ${ } _ { 38 } ^ { 94 } \mathrm { Sr } : \quad 93.915367 \mathrm { u }$ ${ } _ { 92 } ^ { 235 } \mathrm { U } : \quad 235.043924 \mathrm { u }$ ${ } _ { 0 } ^ { 1 } \mathrm { n } : \quad 1.008665 \mathrm { u }$ How much energy is released in this reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

Determine the missing product $X$ in the following nuclear reaction: ${ } _ { 8 } ^ { 16 } \mathrm { O } +$ neutron $\rightarrow \mathrm { X } +$ alpha particle

What is the meaning of the term "critical mass" in regard to nuclear fission?

If a nuclear fission reactor produces an average power of $1.0 \mathrm{GW}$ over the course of a year, what mass of is used up for a 365 -day year if $200 \mathrm{MeV}$ are released per fission reaction?

Determine the missing product $X$ in the following nuclear reaction: ${ } _ { 92 } ^ { 235 } \mathrm { U } +$ neutron $\rightarrow { } _ { 56 } ^ { 141 } \mathrm { Ba } + \mathrm { X } + 3$ neutrons

A nuclear explosion results in a mass decrease of $2.10 \mathrm {~g}$ . How much energy is released during this explosion? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions. One such reaction is ${ } _ { 92 } ^ { 235 } \mathrm { U } + { } _ { 0 } ^ { 1 } \mathrm { n } \rightarrow { } _ { 54 } ^ { 140 } \mathrm { Xe } + { } _ { 38 } ^ { 94 } \mathrm { Sr } + 2 { } _ { 0 } ^ { 1 } \mathrm { n }$ The following mass values are known: Xe: 139.921620 : 93.915367 : 235.043924 : 1.008665 What mass of uranium is needed to produce a 10-kiloton yield? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } = 1.66054 \times \right.$ $10 ^ { - 27 } \mathrm {~kg}$ , 1-kiloton yield $= 5.0 \times 10 ^ { 12 } \mathrm {~J}$ )