Exam 30: Nuclear Physics and Radioactivity

Suppose the half-life of an isotope is 2 days. You purchase 10 grams of the isotope, but it was produced in a laboratory 4 days before it was delivered to you. How much of this isotope will you have 3 days after it was delivered to you?

Rutherfordium-261 has a half-life of $1.08 \mathrm {~min}$ . What is the decay constant of rutherfordium-261 in terms of seconds?

In the first nuclear reaction observed, physicists saw an alpha particle $( Z = 2 )$ interact with a nitrogen nucleus in air $( Z = 7 )$ to produce a proton. The energy of the alpha particle was $55 \mathrm { MeV }$ , enough to enable the nuclei to touch in spite of the Coulomb repulsion. What distance (in fm) between the centers of the alpha particle and the nitrogen was reached? This determines a limit on the radius of the nitrogen nucleus. $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \right.$ $\cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A thallium source with a half-life of $3.7$ years was certified at $10 \mathrm { kBq }$ ten years ago. What is its activity now?

The decay constant of a radioactive isotope is $1.60 \times 10 ^ { - 3 } \mathrm {~s} ^ { - 1 }$ . At a given instant, the number of atoms of the radioactive isotope is $1.85 \times 10 ^ { 12 }$ . How many atoms of the isotope remain after a time interval of $30.0$ minutes?

Which of the following statements is not true of the strong nuclear force?

A radioactive substance containing $4.0 \times 10 ^ { 16 }$ unstable atoms has a half-life of $2.0$ days. What is its activity (in curies, Ci) after $1.0$ day? ( $\mathrm { Ci } = 3.70 \times 10 ^ { 10 } \mathrm {~Bq}$ )

When an unstable nucleus decays by emitting an alpha particle, the atomic mass number $A$ of the nucleus

The decay constant of a radioactive nuclide is $4.6 \times 10 ^ { - 3 } \mathrm {~s} ^ { - 1 }$ . What is the half-life of this isotope, in minutes?

The primary reason that very large nuclei are unstable is due to

Suppose that starting with ${ } _ { 89 } ^ { 227 }$ , the following sequence of decays occurs: first an alpha decay, then a beta-minus decay, and finally another alpha decay. What isotope is left after each one of the decays?

When a stationary plutonium-239 nucleus decays into a uranium-235 nucleus plus an alpha particle, the energy released in the process is $5.24 \mathrm { MeV }$ . The following masses are known: ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ ${ } _ { 92 } ^ { 235 } \mathrm { U } : \quad 235.043924 \mathrm { u }$ What is the kinetic energy of the ${ } _ { 92 } ^ { 235 } \mathrm { U }$ nucleus? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

Radium-226 decays into radon-222 plus an alpha particle. The relevant masses are ${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$ Rn: 222.017570u Ra: 226.025402u How much energy is released in this process? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

The neutral ${ } _ { 13 } ^ { 27 } \mathrm { Al }$ atom has a mass of $26.981539$ u; a neutral hydrogen atom has a mass of $1.007825$ u; a neutron has a mass of $1.008665 \mathrm { u }$ ; and a proton has a mass of $1.007277 \mathrm { u }$ . What is the binding energy per nucleon for ${ } _ { 13 } ^ { 27 } \mathrm { Al }$ ? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } \right)$

A $\beta ^ { + }$ particle is also known as

How long would it take $4.00 \times 10 ^ { 20 }$ atoms to decay to $1.00 \times 10 ^ { 19 }$ atoms if their half-life was $14.7$ years?

How many nucleons would you expect a nucleus to contain if its diameter is 13.4 fm?

A test tube of an isotope having a decay constant of $0.765 \times 10 ^ { - 6 } \mathrm {~s} ^ { - 1 }$ contains $3.0 \times 10 ^ { 17 }$ nuclei of this isotope. (a) What is the half-life of this isotope? (b) What is the initial activity (in Bq) of the isotope? (c) What is the activity of the isotope after 12 days?

The neutral helium atom, ${ } _ { 2 } ^ { 4 }$ He, has a mass of $4.002603 \mathrm { u }$ , a neutron has a mass of $1.008665 \mathrm { u }$ , a proton has a mass of $1.007277 \mathrm { u }$ , and a neutral hydrogen atom has a mass of $1.007825 \mathrm { u }$ . What is the binding energy of the ${ } _ { 2 } ^ { 4 } \mathrm { He }$ nucleus? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } \right)$