1 Nuclear Structure

Tipler Chapter 40 Name: ______

#1 Nuclear Structure

A certain atom has atomic number Z = 26 and atomic mass number A = 58.

(a) How many protons and how many neutrons are in this particular nucleus? b) What is the approximate radius of the nucleus of this atom?

(c) What is the magnitude of the electrostatic force of repulsion between two protons on opposite sides of the diameter of this nucleus?

#2 Taking Apart an Alpha Particle

An alpha () particle is the nucleus of a 4He atom and consists of 2 neutrons and two protons bound together. Let's take apart an -particle, step by step, looking at the energy required at each step. To do so, we may want to use the following atomic masses:

4He 3H 2H p n 4.0026 u 3.01605 u 2.01410 u 1.00783 u 1.08665 u

(a) What is the energy required to remove the first proton?

(b) With that first proton already removed, what is the energy required to remove the first neutron?

(c) Finally, what is the energy required to separate the remaining neutron and proton?

(d) What is the total binding energy of the of the - particle?

(e) What is the total binding energy per nucleon for the  -particle?

#4 Gallium Decay

An isotope of gallium, 67Ga, has an atomic number of 31 and a half-life of 78 hours. The atomic mass of 67Ga is 66.792 u. Consider a small mass of 3.5 grams for 67Ga which is initially pure.

(a) Initially, what is the half-life of the gallium?

(b) Initially, what is the mean life time of the Ga atom in the sample?

(c) Initially, what is the decay rate of the gallium?

(d) What is the half-life of the gallium after 48 hours?

(e) What is the mean life time of the Ga atom in the sample after 48 hours? (f) What is the decay rate of the gallium after 48 hours?

#5 Radioactive Dating

Uranium-238, 238U, decays radioactively via a very long chain of decays, eventually winding up as an isotope of lead, 206Pb.

238U → 206Pb + (many other decay products)

The half-life of this decay chain is 4.47 X 109 years and can normally be considered one long single decay since the first decay takes up most of the time. A rock is found to currently contain 4.2 mg of 238U and 200 mg of 206Pb, but was known to contain no lead at its original formation.

(a) Approximating the 238 decay chain as one single decay, how many 238U atoms did the rock contain at formation?

(b) How old is the rock? c) A rock is thought to be 260 million years old. If it contains 375 mg of 238U, how much 206Pb should it contain?

#5 Decay Chains

The isotope Uranium-235 also transmutates through a series alpha and beta-minus decays and finally ends up as a stable isotope. One complete decay process that occurs involves 7 alpha and 4 beta-minus emissions in the following order:

,  –,  ,  ,  –,  ,  ,  ,  –,  ,  –,

(a) What are the atomic number and atomic mass number of the isotope after the first four particles in the decay process above are emitted?

(b) What are the atomic number and atomic mass number of the isotope after the first eight particles in the decay process above are emitted? c) What are the atomic number and atomic mass number of the isotope at the end of the decay chain?

A different uranium isotope, 238U, decays through a series of alpha and beta-minus decays into the stable isotope of 206Pb. d) How many -decays and how many  –-decays occurs in this decay chain?