Chapter 19, Problem 19.99CP

Interpretation Introduction

Interpretation:

Calculating mass defect and thus calculating the energy released by using Einstein’s equation.

Concept introduction:

Einstein’s equation
It states that any reaction produces or consumes energy due to a loss or gain in mass. Energy and mass are equivalent.
$\Delta E=\Delta m{c}^2$
$\Delta E$ is the change in energy in joules
$\Delta m$ is the change in mass in kg
c is the speed of light

Given:

Boron neutron-capture therapy for cancer treatment
Kinetic energy of Reactants = 0
Kinetic energy of Products = 2.31 MeV
$B+n\stackrel{}{\to }He+Li+\gamma$

Relevant masses

$\begin{array}{l}B=10.012937u\\ e^{-}=0.0005486u\\ He=4.002603u\\ n=1.008665u\\ Li=7.016004u\end{array}$

To determine:

To determine the energy of $\gamma$ released