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NCERT Class XI Chemistry Structure of Atom Solutions

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Question : 44 of 67
Marks: +1, -0
An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than electrons. Assign the symbol of this ion.
Solution:  
Let the number of protons(p) = x
∴ Number of electrons (e) = x – 3 (because the ion carries 3 units of positive charge, it will have 3 electrons less than the number of protons.)
Number of neutrons(n)
= (x - 3) + (x−3)30.4100\frac{(x-3)30.4}{100} = 100(x−3)+(x−3)30.4100\frac{100(x-3)+(x-3)30.4}{100}
n = 100x−300+30.4x−91.2100\frac{100x-300+30.4x-91.2}{100} = 130.4x−391.2100\frac{130.4x-391.2}{100}
We know that A = p + n
56 = x + 130.4x−391.2100\frac{130.4x-391.2}{100} or 56 = 100x+130.4x−391.2100\frac{100x+130.4x-391.2}{100}
or 5600 = 230.4x – 391.2 or 5600 + 391.2 = 230.4x or 5991.2 = 230.4x
∴ x = 5991.2230.4\frac{5991.2}{230.4} = 26
Thus, number of protons (p) = 26, number of electrons (e) = 26 – 3 = 23
therefore, symbol of the ion =  2656Fe3+\,\mathrm{^{56}_{26}Fe^{3+}}
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