Question

How would you balance the following nuclear reaction: $${}_4^{9}Be+{}_2^{4}He\to ??+{}_0^{1}n$$ ?

Answer 1

Hint:Actually we have to know that a nuclear reaction can be termed as the changes that take place in nuclei which results in change of their atomic numbers, mass numbers, or energy states. Also for determining a particular nuclear reaction, we actually use an equation which in turn identifies the nuclides involved in the reaction, their mass numbers and that of other particles that are involved in the reaction. A nuclear reaction is balanced by following the principle of law of conservation of mass but can be in two ways in which the reaction includes addition of atomic mass as well as addition of atomic number. Superscript and subscript of nuclear equations are important as they denote mass number and atomic number respectively.

Complete answer:
Before proceeding to steps of balancing the nuclear equation, let us at first write down the given nuclear reaction.
$${}_4^{9}Be+{}_2^{4}He\to ??+{}_0^{1}n$$
We have to know that in the case of $${}_4^{9}Be$$ , $$Be$$ is the element itself and number $$9$$ which is the superscript denotes the mass number and that of number $$4$$ which is the subscript denotes the atomic number. The same is applicable in $${}_2^{4}He$$.
The steps of balancing the reaction will include addition of atomic mass as well as addition of atomic number by following conservation laws which here helps us to find the unknown one also.
Next we shall proceed through the steps of balancing and can find out the unknown one in the given nuclear reaction.
So, let us add the mass number and atomic number of $$Be$$ and $$He$$ so as it should be in a balance with the product side also . Hence we should be alert during addition of mass number and atomic number in reactant side so that the same addition which we will do in product side should be same to value of atomic number and mass number in reactant side as no single value should not be more or less but should be equal. This is because then only the law of conservation of mass will be successfully processed here. Now, let us go through the steps regarding this.
$${}_4^{9}Be+{}_2^{4}He\to {}_{4+2}^{9+4}x+{}_0^{1}n$$
Now the equation will be as follows,
$${}_4^{9}Be+{}_2^{4}He\to {}_6^{13}x$$
But we have to remember that , here we also have $${}_0^{1}n$$ . But , the problem is as looking on the above equation, we cannot add $${}_0^{1}n$$ there as it will not get balanced and hence cannot follow conservation law because , if we add $${}_0^{1}n$$ the product side magnitude will be unequal to reactant side. On the other hand we cannot leave $${}_0^{1}n$$ as it should be there because then only the given nuclear reaction will be complete. Therefore , what we can do here is to just subtract the mass number and atomic number of neutrons from $${}_6^{13}x$$ and can still keep the neutron in the product side so as to get balanced on both sides. So the further balancing will be as follows,
$${}_4^{9}Be+{}_2^{4}He\to {}_{6-0}^{13-1}x+{}_0^{1}n$$
Now the equation becomes,
$${}_4^{9}Be+{}_2^{4}He\to {}_6^{12}x+{}_0^{1}n$$
From the above equation, we can see the mass number of the unknown element is $$12$$ and the main point to note here is that we can see the atomic number of unknown is $$6$$. We know the element with atomic number $$6$$ is definitely carbon. Hence the unknown element is carbon.
Therefore the final balanced nuclear reaction is as follows,
 $${}_4^{9}Be+{}_2^{4}He\to {}_6^{12}C+{}_0^{1}n$$
In this way, we would balance a nuclear reaction.

Note:First of all for balancing a nuclear reaction, we should know the steps which includes addition of atomic number and mass number of both reactant and product side which should ensure whether both sides are in an equal ratio. Next we have to keep in mind while doing balancing of nuclear reactions that balancing is actually undergoing by following conservation laws. Next important thing we should do is to adjust the calculation by subtracting the atomic number and mass number of neutrons from the unknown element in the product side so as to get balanced with the reactant side. Then only the equation will get balanced without leaving the neutron which may be considered as an excess one in a particular step as we did in the above problem. The same method of balancing can be followed in doing with any kind of balancing problem regarding nuclear reaction. Also the unknown element can be identified from the pre final equation by noting the atomic number of the unknown element at that step.