Exam 30: Nuclear Physics and Radioactivity

Isotope A has a decay constant of $0.723 \mathrm {~s} ^ { - 1 }$ and isotope B has a decay constant of $0.514 \mathrm {~s} ^ { - 1 }$ . Which isotope has a longer half-life?

The decay rate of a radioactive sample decreases from $175 \mathrm { kBq }$ to $12.4 \mathrm { kBq }$ in $18.3 \mathrm {~s}$ . Wha is the half-life of this sample?

In a head-on collision, an alpha particle $( Z = 2 )$ of energy $8.20 \mathrm { MeV }$ bounces straight back from a nucleus of charge $80.0 \mathrm { e }$ . How close were the centers of the objects at closest approach? $( 1 \mathrm { eV } = 1.60$ $\times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

When an unstable nucleus decays by emitting an alpha particle, the atomic number $\mathrm { Z }$ of the nucleus

The main reason that there is a limit to the size of a stable nucleus is

When a $\beta ^ { - }$ particle is emitted from an unstable nucleus, the atomic mass number of the nucleus

If an atomic nucleus containing 64 nucleons has a mass density $\rho$ , what will be the expected mass density of a nucleus containing 512 nucleons?

The half-life of cobalt-60 is $5.3$ years, while that of strontium-90 is about 29 years. Suppose you have samples of both isotopes, and that they initially have the same activity (number of decays per second). What must be true of the numbers of cobalt-60 and strontium-90 nuclei in these samples?

The diameter of an atom is $1.4 \times 10 ^ { - 10 } \mathrm {~m}$ and the diameter of its nucleus is $1.0 \times 10 ^ { - 14 } \mathrm {~m}$ . What fraction of the atom's volume is occupied by its nucleus?

Rutherfordium-261 has a half-life of $1.08 \mathrm {~min}$ . How long will it take for a sample of rutherfordium to lose one-third of its nuclei?

A nucleus ${ } _ { M } ^ { N } X$ undergoes one alpha decay followed by 3 beta-minus decays. (a) What is the resulting nucleus in terms of $\mathrm { M }$ and $\mathrm { N }$ ? (b) If there had been 3 beta-plus decays instead of the beta-minus decays, what would have been the resulting nucleus in terms of $M$ and $N$ ?

Write the standard nuclear notation for the following nuclei: hydrogen-2, sulfur-33, and lead-207.

A beryllium-8 nucleus at rest undergoes double alpha decay as follows: ${ } _ { 4 } ^ { 8 } \mathrm { Be } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 2 } ^ { 4 } \mathrm { He }$ The known atomic masses are: ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ ${ } _ { 4 } ^ { 8 } \mathrm { Be } : \quad 8.005305 \mathrm { u }$ What is the kinetic energy of each departing alpha particle? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

When a $\beta$ - particle is emitted from an unstable nucleus, the atomic number of the nucleus

Polonium-216 decays to lead-212 by emitting what kind of nuclear radiation?

The nuclei of ${ } _ { 2 } ^ { 4 } \mathrm { He }$ are also known as

Suppose that in a certain collection of nuclei there were initially 1024 billion nuclei, and $20.0$ minutes later there was only $1.00$ billion nuclei left, the others having decayed. On the basis of this information, how many nuclei would you estimate decayed in the first $6.00$ minutes?

The symbol for a certain isotope of strontium is ${ } _ { 38 } ^ { 90 } \mathrm { Sr }$ . What is the mass number of this isotope?