Nuclear Chemistry - Equations & Problems | Formulas@MathCaptain.com

The reactions which effects the nucleus of an atom is called as nuclear reaction. The major difference between chemical reactions and nuclear reactions are that nucleus of atom does not involve in chemical reactions but electrons of orbit involve in such reactions whereas nucleus take part in nuclear reaction.

Chemical reactions involve exchange of electrons from one or more substances to form different substance. Nuclear reactions involve change in the nucleus to form another element by gain or lose some particles. We know that an atom contains a nucleus with protons and neutrons. Electrons are placed in energy shells around the nucleus. In nuclear reactions, unstable nuclei changes to stable nuclei by giving off a lot of energy to form more stable with the emission of alpha, beta, positron particles and gamma rays.

In chemistry nuclear equations are balanced equations with same number of total of the atomic numbers and the total of the mass numbers on both sides of the equation. Some nuclear chemistry examples are as given below;

$_{8}^{17}\textrm{O} + _{6}^{12}\textrm{C} \rightarrow _{8}^{16}\textrm{O} + _{6}^{13}\textrm{C}$ --------------- (1)

$_{1}^{2}\textrm{H} + _{10}^{20}\textrm{Ne} \rightarrow _{1}^{1}\textrm{H} + _{10}^{21}\textrm{Ne}$ ----------------(2)

$_{1}^{2}\textrm{H} + _{7}^{14}\textrm{N} \rightarrow _{2}^{3}\textrm{He} + _{6}^{13}\textrm{C}$ --------------(3)

$_{2}^{4}\textrm{He} + _{7}^{14}\textrm{N} \rightarrow _{8}^{17}\textrm{O} + _{1}^{1}\textrm{H}$ ---------------(4)

$_{2}^{4}\textrm{He} + _{4}^{9}\textrm{Be} \rightarrow _{6}^{12}\textrm{C} + n$ --------------(5)

$_{1}^{1}\textrm{H} + _{7}^{15}\textrm{N} \rightarrow _{1}^{1}\textrm{H} + _{7}^{14}\textrm{N} + _{0}^{1}\textrm{n}$ ----------------(6)

$n + _{13}^{27}\textrm{Al} \rightarrow _{13}^{28}\textrm{Al}$ ---------------(7)

The nuclear chemistry problems are mainly based on either balancing the nuclear reactions or calculation of decay rate.

Example 1: A sample of Cu-61 contains 4.35 $\times$ 10$^{-5}$ mol and emits 2.07 $\times$ 10$^{19}$ positrons in 90.0 minutes. Calculate the number of atoms before any decay and percent of undecayed nuclei after emission of given positron particles.

Solution:

Before decay, there are 4.35 $\times$ 10$^{-5}$ mol that is 4.35 $\times$ 10$^{-5}$ mol $\times$ 6.022 $\times$ 10$^{23}$ atoms/mol = 2.619 $\times$ 10$^{19}$ atoms. The amount of undecayed element after emission of given positions would be;

$\frac{2.07 \times 10^{19}}{2.619 \times 10^{19}}$ = 0.790 (this is the amount that did decay.)

1 - 0.790 = 0.21 = 21%

Example 2: Calculate the decay constant of Ga-67 whose half-life is 67.15 hr.

Solution:

k = $\frac{(ln 2)}{t_{1/2}}$

k = $\frac{(ln 2)}{67.15 \ hr}$

k = 0.01032 hr$^{-1}$.