Question

If mass of neutron is assumed to half of its original value, whereas that of proton is assumed to be twice of its original value, then the atomic mass of $_6^{14}C$ will be:
A: Same
B:\[14.28\% \]more
C:\[14.28\% \]
D: \[28.56\% \]less

Answer 1

Hint: An atom comprises a nucleus having neutrons and protons which are surrounded by electrons in orbits. Number of protons (atomic number) can be considered to be equal to the total number of electrons in a neutral atom (denoted as\[Z\]). Whereas, the summation of the number of neutrons and number of protons equals the mass number of an atom (denoted as\[M\]). Thus, the number of neutrons =\[M - Z\].

Complete step by step answer:
 In the given question, we know the value of mass number (\[M\]) and atomic number (\[Z\]) of the atom i.e. $_6^{14}C$which are mentioned below:
\[
  M = 14 \\
  Z = 6 \\
\]
We know that atomic number is equal to the number of protons i.e. 6 in the present case. And, number of neutrons can be found out by subtracting the number of protons from the mass number.
Number of neutrons$ = M - Z = 14 - 6 = 8$
Now as per the information given in the question, mass of neutron becomes halved while mass of proton becomes doubled i.e.
New mass of proton\[ = 6 \times 2 = 12\]
New mass of neutron\[ = \dfrac{8}{2} = 4\]
Now, using this information, we have to find out the new atomic mass of $_6^{14}C$.
New atomic mass\[ = 12 + 4 = 16\]
\[\% {\text{ }}increase{\text{ }}in{\text{ }}mass = \dfrac{{16 - 14}}{{14}} \times 100 = 14.28\% \]

So, the correct answer is Option B.

Note: Each atom of a given element has the similar number of protons while atoms of distinct elements possess distinct numbers of protons. An atom consists of the same number of protons as well as electrons. As protons as well as electrons possess equal and opposite electrical charges, atoms have no overall electrical charge (i.e. neutral).