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Chapter 7: Problem 18

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the \(n=3\) electron shell: \(\mathrm{K}, \mathrm{Mg}, \mathrm{P}, \mathrm{Rh} , \mathrm{Ti}.\)

Short Answer

Expert verified
The atoms arranged in the order of increasing effective nuclear charge experienced by the electrons in the n=3 electron shell are: Mg, P, K, Ti, Rh.

Step by step solution

01

Determine the atomic numbers

To find the effective nuclear charge, we first need the atomic numbers (Z) of the given elements. The atomic numbers can be found using a periodic table. The atomic numbers of the given elements are: K: 19 Mg: 12 P: 15 Rh: 45 Ti: 22
02

Calculate the number of inner electrons (shielding electrons)

We next determine the number of electrons in the inner shells, which shield the outer electrons from the full positive charge of the nucleus. For the n=3 electron shell, there will be two inner shells (n=1 and n=2), with a total of 10 electrons (2 electrons in n=1 and 8 electrons in n=2).
03

Calculate the effective nuclear charges (Z_eff)

The effective nuclear charge (Z_eff) for electrons in the n=3 shell can be calculated using the following formula: \(Z_\text{eff} = Z - S\) Where Z is the atomic number and S is the number of shielding electrons. For our elements, the Z_eff values are: K: 19 - 10 = 9 Mg: 12 - 10 = 2 P: 15 - 10 = 5 Rh: 45 - 10 = 35 Ti: 22 - 10 = 12
04

Arrange the elements in the order of increasing Z_eff

Now, we will arrange the elements in the order of increasing effective nuclear charge experienced by the electrons in the n=3 electron shell: Mg (2) < P (5) < K (9) < Ti (12) < Rh (35) So, the given atoms arranged in the order of increasing effective nuclear charge are: Mg, P, K, Ti, Rh.

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Most popular questions from this chapter

(a) Does metallic character increase, decrease, or remain unchanged as one goes from left to right across a row of the periodic table? (b) Does metallic character increase, decrease, or remain unchanged as one goes down a column of the periodic table? (c) Are the periodic trends in (a) and (b) the same as or different from those for first ionization energy?

Silver and rubidium both form \(+1\) ions, but silver is far less reactive. Suggest an explanation, taking into account the ground-state electron configurations of these elements and their atomic radii.

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) Ba, Ca, Na; (b) In, Sn, As; (c) Al, Be, Si.

Consider the stable elements through lead (Z = 82). In how many instances are the atomic weights of the elements out of order relative to the atomic numbers of the elements?

Among elements 1-18, which element or elements have the smallest effective nuclear charge if we use Equation 7.1 to calculate \(Z_{\text { eff}}\)? Which element or elements have the largest effective nuclear charge?
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