Question 43 of 62intermediate🔧 ApplyNumerical2 marks

An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than electrons. Assign the symbol to this ion.

Correct Answer

2656Fe3+^{56}_{26}\text{Fe}^{3+}

Exercise: EXERCISES | Q: 2.44 | (Page 41)
For More Understanding

Explanation

To find the symbol of the ion, we use the relationship between mass number, atomic number, and the number of neutrons and electrons. The mass number is the sum of protons and neutrons. For a positively charged ion, the number of electrons is less than the number of protons. By setting up an equation based on the given percentage difference between neutrons and electrons, we can solve for the atomic number and assign the correct symbol.

Solution Steps

  1. Step 1: Let the number of protons (atomic number) be ZZ. Since the ion has 3 units of positive charge, the number of electrons is e=Z−3e = Z - 3.

  2. Step 2: The mass number is A=56A = 56. The number of neutrons is n=A−Z=56−Zn = A - Z = 56 - Z.

  3. Step 3: The ion contains 30.4% more neutrons than electrons, so n=e+0.304e=1.304en = e + 0.304e = 1.304e. Substituting the values gives 56−Z=1.304(Z−3)56 - Z = 1.304(Z - 3).

  4. Step 4: Solving the equation: 56−Z=1.304Z−3.912⇒59.912=2.304Z⇒Z=2656 - Z = 1.304Z - 3.912 \Rightarrow 59.912 = 2.304Z \Rightarrow Z = 26.

  5. Step 5: The atomic number Z=26Z = 26 corresponds to the element Iron (Fe). Therefore, the symbol of the ion is 2656Fe3+^{56}_{26}\text{Fe}^{3+}.

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