Question

An ion with mass number 56 contains 3 units of positive charge and \[30.4\% \] more neutrons than electrons. What would be the symbol of this ion?
A. \[_{26}^{56}F{e^{ + 3}}\]
B. \[_{26}^{56}F{e^{ + 2}}\]
C. \[_{27}^{56}C{o^{ + 2}}\]
D. \[_{27}^{58}C{o^{ + 3}}\]

Answer 1

Hint: For any atom, ion, element atomic weight is sum of proton number and neutron number . This means the total number of neutrons and protons is equal to its atomic weight or mass number. Now the number of the proton is equal to the number of electrons of a neutral atom.

Formula used: \[A = {\text{ }}X{\text{ }} + {\text{ }}N{\text{ }}\] where, A is the atomic weight, X is the proton number. N is the neutron number.

Complete step by step answer:
Now, if the electron gets removed from the atom a positive charge is developed. But the number of protons remains the same. The number of positive charges is equivalent to the number of electrons removed from the atom.
From the given information, the mass number of that ion is 56. And the positive charge is +3.
Now let the total number of electron of that atom is X. therefore the number of the electron remains in that ion is \[(X - 3)\]. Now the total number of the proton is X.
Now according to the question, the number of neutron increases by \[30.4\% \]of the remaining electrons, therefore, the total number of the neutron is \[(X - 3) \times \dfrac{{30.4}}{{100}} + (X - 3)\]. Now according to the formula, \[A = {\text{ }}X{\text{ }} + {\text{ }}N{\text{ }}\].
Find out the value of X as follows.
\[
  A = {\text{ }}X{\text{ }} + {\text{ }}N{\text{ }} \\
  56 = (X - 3) \times \dfrac{{30.4}}{{100}} + (X - 3) + {\text{ }}X \\
  56 = (X - 3)\left( {\dfrac{{30.4}}{{100}} + 1} \right) + {\text{ }}X \\
  56 = (X - 3)\left( {1.304} \right) + {\text{ }}X \\
  56 = 3.912 + {\text{ }}2.304X \\
  59.912 = {\text{ }}2.304X \\
  26 = {\text{ }}X \\
 \]
So, the atomic number or proton number of that atom is 26. Which is for iron (Fe).
So, the symbol of this ion is, \[_{26}^{56}F{e^{ + 3}}\]

Therefore, the correct option is A.

Note:
According to the Bohr's model in the atoms, the electron is moving around the nucleus in different shells. These shells are K, L, M, N, etc. Electronic distribution of an atom/ion is an arrangement in a space of the electrons around the center of the mass(nucleus) of the atom or ion among the orbits or shells.