Exam 30: Nuclear Physics and Radioactivity

Estimate the radius of a nucleus with mass $50 \mathrm { u }$ . ( $m _ { \text {neutron } } \approx m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

Two radioactive isotopes, X and Y, both decay to stable products. The half-life of X is about a day, while that of Y is about a week. Suppose a radioactive sample consists of a mixture of these two Nuclides. If the mixture is such that the activities arising from X and Y are initially equal, then a few Days later the activity of the sample will be due

The atomic mass unit is defined as

One of the fusion reactions that occurs in the sun is: ${ } _ { 2 } ^ { 3 } \mathrm { He } + { } _ { 2 } ^ { 3 } \mathrm { He } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 1 } ^ { 1 } \mathrm { H } + { } _ { 1 } ^ { 1 } \mathrm { H }$ The following atomic masses are known: ${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.007825 \mathrm { u }$ ${ } _ { 2 } ^ { 3 } \mathrm { He } : \quad 3.016029 \mathrm { u }$ ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ What is the reaction energy released in this fusion reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

The half-life of a radioactive material is $4.5$ days. How many days are required for a sample, with an initial activity of $1.0 \times 10 ^ { 5 } \mathrm {~Bq}$ , to decay to an activity of $100 \mathrm {~Bq}$ ?

One material used in nuclear bombs is $239 \mathrm { Pu }$ , with a half-life of 24,000 years. How long must we wait for a buried stockpile of this substance to decay to $1 / 1000$ of its original activity?

Bismuth ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ is known to be radioactive. The stability of ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ with respect to alpha, beta-plus and beta-minus decay is to be determined. The following atomic masses are known: : 4.002603 : 207.981998 : 211.991871 : 211.991255 : 211.988842 The Bi nucleus is

Isotope A has a decay constant of $0.861 \mathrm {~s} ^ { - 1 }$ and isotope B has a decay constant of $0.627 \mathrm {~s} ^ { - 1 }$ . Which isotope has a longer mean life (time constant)?

What is the mass number of alpha particles?

The stability of ${ } _ { 17 } ^ { 36 } \mathrm { Cl }$ with respect to alpha, beta-plus and beta-minus decay is to be determined. The following atomic masses are known: ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ ${ } _ { 15 } ^ { 32 } \mathrm { P } : \quad 31.973907 \mathrm { u }$ ${ } _ { 16 } ^ { 36 } \mathrm {~S} : \quad 35.967081 \mathrm { u }$ ${ } _ { 17 } ^ { 36 } \mathrm { Cl } : \quad 35.968307 \mathrm { u }$ ${ } _ { 18 } ^ { 38 } \mathrm { Ar } : \quad 35.967546 \mathrm { u }$ The ${ } _ { 17 } ^ { 36 } \mathrm { Cl }$ nucleus is

A $\beta ^ { - }$ decay occurs in an unstable nucleus when

A proton is projected at a stationary ${ } _ { 88 } ^ { 226 }$ Ra aluminum target. The proton momentarily comes to a halt at a distance from the center of an aluminum nucleus, equal to twice the nuclear radius. Assume that the nucleus retains its spherical shape and that the nuclear force on the proton is negligible. The initial kinetic energy of the proton, in $\mathrm { MeV }$ , is closest to:

The unstable isotope 234Th decays by $\beta$ emission with a half-life of $24.5$ days. If the initial decay rate of the sample is $6.2 \times 10 ^ { 17 } \mathrm {~Bq}$ , what is the decay rate after 37 days?

The stability of ${ } _ { 6 } ^ { 11 } \mathrm { C }$ with respect to alpha, beta-plus and beta-minus decay is to be determined. The following atomic masses are known: ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ ${ } _ { 4 } ^ { 7 } \mathrm { Be } : \quad 7.016928 \mathrm { u }$ ${ } _ { 5 } ^ { 11 } \mathrm {~B} : \quad 11.009305 \mathrm { u }$ ${ } _ { 6 } ^ { 11 } \mathrm { C } : \quad 11.011433 \mathrm { u }$ ${ } _ { 7 } ^ { 11 } \mathrm {~N} : \quad 11.026742 \mathrm { u }$ The ${ } _ { 6 } ^ { 11 } \mathrm { C }$ nucleus is

In a laboratory accident, a work area is contaminated with radioactive material. Health physicists monitor the area during a 30-day period and obtain the data shown in the table. The accident occurred at time $t = 0$ days. They determine that it will not be safe for workers to enter the area until the radioactivity level has dropped to 16 counts per minute. Of the choices listed, which one is the earliest time after the accident that workers could safely return?

Fermium-253 has a half-life of $3.00$ days. If a sample of fermium originally has $7.37 \times 10^7$ nuclei, how long will it take for there to be only $3.36 \times 10^6$ fermium-253 nuclei left in this sample?

What are the mass number A and the charge (in units of e) for each of the following particles or rays? (a) beta-plus (b) beta-minus (c) gamma ray

The isotope ${ } _ { 92 } ^ { 235 } \mathrm { U }$ is radioactive and decays in a series to ${ } _ { 90 } ^ { 227 }$ Th. In this series, the particles ejected from the nucleus are

If an atomic nucleus containing 64 nucleons has a radius $R$ , what will be the expected radius of a nucleus containing 512 nucleons?

A radioactive source emits $2.4 - \mathrm { MeV }$ neutrons at the rate of 7100 neutrons per second. The number of atoms in the source is $2.6 \times 10 ^ { 9 }$ . What is the activity of the source, in curies (Ci)? $( 1.00 \mathrm { Ci } = 3.70 \times$ $10 ^ { 10 } \mathrm {~Bq}$ )