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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# A recently named element is darmstadtium (Ds), which has electrons. Assume that you can put 110 the electrons into the atomic shells one by one and can neglect any electron-electron interaction. With the atom in the ground state, what is the spectroscopic notation for the quantum number for the last electron?

The spectroscopic notation for the quantum number I for the last electron is g.

See the step by step solution

## Step 1: The given data:

The element is darmstadtium (Ds), which has 110 electrons.

Assumption- All the electrons are put into the shells one by one and electron-electron interaction is neglected.

## Step 2: Understanding the concept of the configuration of an atom:

An atom is a particle of a substance that specifically defines an achemical element. An atom consists of a central nucleus usually surrounded by one or more electrons.

The electronic state is defined by the configuration of the electron system, as well as the quantum numbers of each electron that contribute to that configuration. Each electronic state corresponds to one of the molecular energy levels

Using the concept of the electron states, the values of the electrons are to be accommodated in each shell with the different quantum numbers ranging from 1,2,3,4,5, and other higher orders. Thus, the order of the subshells is named as s,p,d,f,g, and to the higher values.

Formula:

The number of electron states presents in the shell for each given value of is,

$N=2{n}^{2}$ ….. (1)

## Step 3: Calculation for the spectroscopic notation of the given element:

If ignore the electron-electron interaction, the element notation with electrons using equation (1). Thus, the two electrons are in the n=1 shell, eight electrons in the shell, in the n=2 shell 18, in the n=3 shell 32, and the n=4 remaining 50(=110-2-8-18-32) in the n=5 shell. The electrons would be placed in the subshells in the order according to the concept and thus the resulting configuration is

$5{s}^{2}5{p}^{6}5{d}^{10}5{f}^{14}5{g}^{18}$.

Hence, the spectroscopic notation for the quantum number of the last electron would be g.

However, for considering the electron-electron interaction, the ground-state electronic configuration of the element is $\left[Rn\right]5{f}^{14}6{d}^{9}7{s}^{1}$.

Where $\left[Rn\right]:1{s}^{2}2{s}^{2}3{s}^{2}3{p}^{6}3{d}^{1}04{s}^{2}4{p}^{6}4{d}^{10}4{f}^{14}5{s}^{2}5{p}^{6}5{d}^{10}6{s}^{2}6{p}^{6}$represents the inner-shell electrons.