Chapter 20, Problem 20.97QP

Interpretation Introduction

Interpretation:

Energy released when 4.50kg of U-235 undergoes given fission process and compare this energy with heat released when 4.50kg graphite burns to Carbon dioxide gas.

Answer to Problem 20.97QP

• Energy released when 4.50kg of U-235 undergoes given fission is $\text{-5}{\text{.419×10}}^{\text{14}}\text{J}$.
• The energy released is high than the energy released by 4.50kg of Carbon.

Explanation of Solution

Given:

Mass of I-136 nuclei = $\text{135}\text{.8401 amu}$

Mass of Y-96 nuclei = $\text{95}\text{.8629 amu}$

$\begin{array}{l}\text{Nuclear mass of U-235= 235}\text{.04392amu-(92×0}\text{.000549amu)=234}\text{.993412amu}\\ \\ \text{Nuclear mass of I-135=135}\text{.8401amu-(53×0}\text{.000549amu)=135}\text{.811003amu}\\ \\ \text{Nuclear mass of Y-96 = 95}\text{.86amu-(39×0}\text{.000549amu)=95}\text{.841489amu}\end{array}$

Write the appropriate nuclear mass below each nuclide symbol and calculate change in mass.

$\begin{array}{l}{}_{\text{0}}^{\text{1}}\text{n }\text{+ }{}_{\text{92}}^{\text{235}}\text{U }\stackrel{}{\to }{}_{\text{53}}^{\text{136}}\text{I }{\text{+ }}_{\text{39}}^{\text{96}}{\text{Y + 4}}_{\text{0}}^{\text{1}}\text{n}\\ \text{Masses: 1}\text{.008665}\text{234}\text{.993412}\text{135}\text{.811003}\text{95}\text{.841489}\text{1}\text{.008665}\text{amu}\\ \\ \text{Δm =}\left[\text{135}\text{.811003+95}\text{.841489+1×008665-(1}\text{.008665+234}\text{.99934120)}\right]\text{amu}\\ \\ \text{= - 0}\text{.314925amu}\end{array}$

When 1 mol U-235 are undergo fission process, the change in mass is $\text{-0}\text{.314925 g}$. Therefore, for 4.50kg of U-235, the mass change is

$\text{4}{\text{.50×10}}^{\text{3}}\text{g U-235×}\frac{\text{1mol U-235}}{\text{235}\text{.04392g U-235}}\text{×}\frac{\text{-0}\text{.314925g}}{\text{1}\text{.00728 U-235}}\text{= -6}\text{.029g}$

Converting mass to energy gives,

$\begin{array}{l}{\text{ΔE=(Δm)c}}^{\text{2}}\text{=(-6}{\text{.029×10}}^{\text{-3}}\text{kg)(2}{\text{.998×10}}^{\text{8}}{\text{m/s)}}^{\text{2}}\\ \\ \text{=-5}{\text{.419×10}}^{\text{14}}\text{J}\\ \end{array}$

For the combustion of Carbon:

$\begin{array}{l}\text{C(graphite)}{\text{+ O}}_{\text{2(g)}}\stackrel{}{\to }{\text{CO}}_{\text{2(g)}}\\ \text{ΔH}\text{0}\text{0}\text{-394kJ/mol}\\ \text{Forthereaction,}\\ \text{ΔH=ΔE=-394kJ/mol}\\ \\ \text{4}{\text{.50×10}}^{\text{3}}\text{g×}\frac{\text{1molC}}{\text{12}\text{.01gC}}\text{×}\frac{\text{-394kJ}}{\text{1mol}\text{C}}\text{= -1}{\text{.476×10}}^5\text{kJ}\\ =-1.48{\text{×10}}^5\text{kJ}\end{array}$

To compare the two quantities, take the ratio of two:

$\begin{array}{l}\frac{\text{E(U-235)}}{\text{E(C(graphite))}}\text{=}\frac{\text{-5}{\text{.419×10}}^{\text{11}}\text{kJ}}{\text{1mol C}}\\ \\ \text{=-1}{\text{.476×10}}^{\text{5}}\text{kJ}\end{array}$

In the fusion process the energy released from $\text{4}\text{.50kg}$ U-235 ( $\text{5}{\text{.42×10}}^{\text{11}}\text{kJ)}$ is more than 3 million times larger than the energy released by burning $\text{4}\text{.50kg}$ of graphite which is equal to $\text{1}{\text{.48×10}}^{\text{5}}\text{kJ}$.

Conclusion

• Energy released when 4.50kg of U-235 undergoes given fission was calculated as $\text{-5}{\text{.419×10}}^{\text{14}}\text{J}$.
• The energy released in this process was high than the energy released by 4.50kg of Carbon.