24.113 CP - Chemistry: Molecular Nature Of Matter And Change

Question

The scene below represents a reaction (with neutrons grey and protons purple) that occurs during the lifetime of a star. 

(a) Write a balanced nuclear equation for the reaction. 

(b) If the mass difference is 7.7x10^-2, find the energy (kJ) released.

Step-by-Step Solution

Answer

(a) The balanced nuclear equation for the reaction is ${}_6{}^{12}C{+}_2^{4}He{\to }_8^{16}O$.

(b) The energy released is $1.1490·{10}^{-14}kJ$ .

 

Step 1: Concept Introduction

A nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to form one or more new nuclides in nuclear physics and nuclear chemistry. As a result, a nuclear reaction must transform at least one nuclide into another.

Step 2: The Balanced Equation

1. Firstly, we have to count the number of neutrons and protons in each of the reacting species and then write the balanced equation for the reaction takes place.

The balanced equation for the reaction is –

${}_6{}^{12}C{+}_2^{4}He{\to }_8^{16}O$

 

Therefore, the balanced equation is obtained.

Step 3: Calculation for Energy

(b)

Binding energies are commonly expressed in mega-electron volts (MeV).

$1MeV={10}^{6}eV=1.602·{10}^{-13}J$

A particularly useful factor converts the atomic mass unit to its energy equivalent in electron volts –

$1amu=931.5·{10}^{6}eV=931.5MeV$

Using the equations above, we can determine the value of energy released in kJ.

$Energy released =7.7·{10}^{-2}amu\left(\frac{931.5MeV}{1amu}\right)\left(\frac{1.602·{10}^{-13}}{1MeV}\right)\left(\frac{1kJ}{1000J}\right)=1.1490·{10}^{-14}kJ$

 

Therefore, the value for energy is obtained as $1.1490·{10}^{-14}kJ$.