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Chapter 28: Problem 43

(a) What are the electron configurations of the ground states of lithium \((Z=3),\) sodium \((Z=11),\) and potassium \((Z=19) ?\) (b) Why are these elements placed in the same column of the periodic table?

Short Answer

Expert verified
Answer: Lithium, sodium, and potassium are placed in the same column of the periodic table because they have the same outer electron configuration, with one electron in their outermost s-orbital. This results in similar chemical properties among these elements, also known as alkali metals.

Step by step solution

01

Determine the electron configuration of Lithium (Z=3)

To find the electron configuration of Lithium, we first look at its atomic number (Z=3) which tells us that it has 3 electrons in the ground state. The electron configuration for Lithium will follow the order in which the atomic orbitals fill, starting with the lowest energy orbital (1s) and going in ascending order (2s, 2p, 3s, 3p, etc.). The electron configuration for Lithium (Z=3) is: \(1s^2 2s^1\)
02

Determine the electron configuration of Sodium (Z=11)

Like we did for lithium, we look at the atomic number of Sodium (Z=11) which tells us that it has 11 electrons in the ground state. The electron configuration following the same order as before, will be: The electron configuration for Sodium (Z=11) is: \(1s^2 2s^2 2p^6 3s^1\)
03

Determine the electron configuration of Potassium (Z=19)

Lastly, we look at the atomic number of Potassium (Z=19) which tells us that it has 19 electrons in the ground state. The electron configuration following the same order will be: The electron configuration for Potassium (Z=19) is: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\)
04

Compare electron configurations and relate to their position in the periodic table

When comparing the electron configurations of lithium (\(1s^2 2s^1\)), sodium (\(1s^2 2s^2 2p^6 3s^1\)), and potassium (\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\)), we can observe that they all have one electron in their outermost s-orbital with electron configurations that differ only in the number of filled inner orbitals. These elements are placed in the same column of the periodic table (alkali metals) because they have the same outer electron configuration, which results in similar chemical properties.

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Most popular questions from this chapter

An electron confined to a one-dimensional box has a ground-state energy of \(40.0 \mathrm{eV} .\) (a) If the electron makes a transition from its first excited state to the ground state, what is the wavelength of the emitted photon? (b) If the box were somehow made twice as long, how would the photon's energy change for the same transition (first excited state to ground state)?
A proton and a deuteron (which has the same charge as the proton but 2.0 times the mass) are incident on a barrier of thickness \(10.0 \mathrm{fm}\) and "height" \(10.0 \mathrm{MeV} .\) Each particle has a kinetic energy of $3.0 \mathrm{MeV} .$ (a) Which particle has the higher probability of tunneling through the barrier? (b) Find the ratio of the tunneling probabilities.
What is the ground-state electron configuration of nickel (Ni, atomic number 28 )?
(a) Show that the number of electron states in a subshell is \(4 \ell+2 .\) (b) By summing the number of states in each of the subshells, show that the number of states in a shell is \(2 n^{2} .\) [Hint: The sum of the first \(n\) odd integers, from 1 to \(2 n-1,\) is \(n^{2} .\) That comes from regrouping the sum in pairs, starting by adding the largest to the smallest: \(1+3+5+\dots+(2 n-5)+(2 n-3)+(2 n-1)\) \(=[1+(2 n-1)]+[3+(2 n-3)]+[5+(2 n-5)]+\cdots\) \(=2 n+2 n+2 n+\cdots=2 n \times \frac{n}{2}=n^{2}\)
An electron moving in the positive \(x\) -direction passes through a slit of width \(\Delta y=85 \mathrm{nm} .\) What is the minimum uncertainty in the electron's velocity in the \(y\) -direction?
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