Chapter 14, Problem 14.59PAE

Interpretation Introduction

a) Interpretation:

The total estimated mass Zr and Te disposed as nuclear waste by the nuclear technician

Concept Introduction: ${}^{235}U$

(uranium) undergoes a fission reaction which is neutron induced. On doing so, it will split into two smaller nuclei ${}^{97}Zr$

(zirconium) and ${}^{137}Te$(tellurium). In the process, neutrons and gamma rays are released. The nuclear equation for this reaction is as follows:

${}_{92}^{235}U{+}_0^{1}n{\to }_{52}^{137}Te{+}_{40}^{97}Zr+2_0^{1}n$

Answer to Problem 14.59PAE

Solution:

3.231 metric ton

Explanation of Solution

The total amount of electrical energy generated by all the nuclear reactors is

$E_n=\frac{19.43}{100}\times 4.1\times {10}^6\times {10}^9\times 3600=2.867868\times {10}^{18}J$

From the problem 14.55, we know the amount of energy released during the fission of 1 kg of ${}^{235}U$ is $8.789748369\times {10}^{14}J$

Hence,

Total mass of ${}^{235}U$ used =$\frac{2.867868\times {10}^{18}}{8.789748369\times {10}^{14}}=3262.741867kg$

For every fission of 236.133 grams of ${}^{235}U$, 233.83627 grams of nuclear waste is generated.

Hence, the total estimated mass of Zr and Te (which are the products of fission of ${}^{235}U$) disposed as nuclear waste is

$\frac{233.83627}{236.133}\times 3263.741867=3231.007051kg/3.231metricton$

Interpretation Introduction

(b) Interpretation:

Whether any of the products Zr and Te obtained from the fission of ${}^{235}U$

are available in measurable quantities in the nuclear waste

Concept Introduction: ${}^{235}U$ (uranium) undergoes a fission reaction which is neutron induced. On doing so, it will split into two smaller nuclei ${}^{97}Zr$ (zirconium) and ${}^{137}Te$ (tellurium). In the process, neutrons and gamma rays are released. The nuclear equation for this reaction is as follows:

${}_{92}^{235}U{+}_0^{1}n{\to }_{52}^{137}Te{+}_{40}^{97}Zr+2_0^{1}n$

Answer to Problem 14.59PAE

Solution:

Only a measurable quantity of Zr will be left in the waste

Explanation of Solution

The half life of ${}^{97}Zr$ is 16.749 hours. The half life of ${}^{137}Te$ is 2.49 seconds. As ${}^{137}Te$ would undergo Beta-minus decay, it would get degraded within 2.49 seconds whereas Zr having larger half life will be present in measurable quantities.

Interpretation Introduction

(c) Interpretation:

Decay series of each isotope ${}^{97}Zr$ and ${}^{137}Te$

Concept Introduction: ${}^{235}U$ (uranium) undergoes a fission reaction which is neutron induced. On doing so, it will split into two smaller nuclei ${}^{97}Zr$(zirconium) and ${}^{137}Te$ (tellurium). In the process, neutrons and gamma rays are released. The nuclear equation for this reaction is as follows:

${}_{92}^{235}U{+}_0^{1}n{\to }_{52}^{137}Te{+}_{40}^{97}Zr+2_0^{1}n$

Answer to Problem 14.59PAE

Solution:

The decay series for Te

Explanation of Solution

The decay series of ${}^{137}Te$ is

The decay series of ${}^{97}Zr$ is

The decay series of ${}^{137}Te$ has Cs 137 which will remain in waste for many years.

Interpretation Introduction

(d) Interpretation:

The difference between the total mass of the waste using the stable isotope products and the technician’s estimated total mass.

Concept Introduction: ${}^{235}U$ (uranium) undergoes a fission reaction which is neutron induced. On doing so, it will split into two smaller nuclei ${}^{97}Zr$ (zirconium) and ${}^{137}Te$ (tellurium). In the process, neutrons and gamma rays are released. The nuclear equation for this reaction is as follows:

${}_{92}^{235}U{+}_0^{1}n{\to }_{52}^{137}Te{+}_{40}^{97}Zr+2_0^{1}n$

Answer to Problem 14.59PAE

Solution:

The technician’s estimates of total waste were off by 0.079751 kg.

Explanation of Solution

Mass of the stable isotope products =$96.906+0.9701\times 136.925+0.0299\times 136.907=233.8305$

Mass of the waste so obtained = $\frac{233.8305}{236.133}\times 3262.741867=3230.9273$ kg or 3.2309273 metric ton

The difference between the technician’s estimated mass and the above calculated mass is

$\Delta M=3231.007051-3230.9273=0.079751kg$