Electronic Configurations

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The Electromagnetic Spectrum

The electromagnetic spectrum is a range of frequencies covering all electromagnetic radiation, divided into regions such as radio, infrared, visible, ultraviolet, X-rays and gamma rays.
All electromagnetic waves travel at the same speed in a vacuum: the speed of light, c = 3.00 × 10⁸ m s⁻¹.
Waves differ in frequency (f) and wavelength (λ); frequency is the number of waves passing per second, and wavelength is the distance between two consecutive peaks.
Frequency and wavelength are inversely related: higher frequency means shorter wavelength, and lower frequency means longer wavelength.
The key relationship is c = fλ; since c is constant, frequency can be calculated from wavelength, or vice versa.
Gamma rays, X-rays and UV are high frequency, high energy radiation that can damage cells and are hazardous to health.

Continuous vs Line Spectra

A continuous spectrum contains all colours of visible light, blending smoothly without gaps in frequency or wavelength.
A continuous spectrum is produced when white light is refracted through a prism or water droplets, as in a rainbow.
A line spectrum shows only certain fixed frequencies of light, indicating that emitted light from atoms is quantised (quanta means 'little packet').
The line spectrum of an element is characteristic of that element, such as the helium spectrum which shows only certain frequencies.

Emission Spectra

Electrons move in energy levels around the nucleus; when they absorb energy they move to higher levels, and they release energy when returning to lower levels.
The frequency of emitted energy matches the frequency of energy absorbed.
If emitted energy is in the visible region, it can be analysed using a diffraction grating to produce a line emission spectrum.
Each line in an emission spectrum corresponds to a specific energy value, suggesting electrons can only possess a limited choice of allowed energies.
In the hydrogen emission spectrum, lines get closer together towards the blue end; this is called convergence, converging towards the higher energy end, corresponding to the ionisation energy.
The visible lines of hydrogen were first observed by Johannes Balmer and are named after him; they correspond to electron jumps from higher levels down to n = 2.
Niels Bohr applied Quantum Theory in 1913, proposing that electrons exist only in fixed energy levels; the hydrogen line spectrum provided evidence for these levels.

Electron Transitions and Regions

Transition from n = ∞ to n = 3: infrared region, low energy.
Transition from n = ∞ to n = 2: visible region, medium energy.
Transition from n = ∞ to n = 1: ultraviolet region, high energy.
Emission in the visible region occurs for an electron jumping from any higher energy level to n = 2.

Energy Levels and Subshells

Electrons are arranged around the nucleus in principal energy levels or principal quantum shells, numbered by principal quantum numbers (n).
The lower the principal quantum number, the closer the shell is to the nucleus; the higher the principal quantum number, the greater the energy of electrons in that shell.
Each principal quantum number can hold a fixed number of electrons: n = 1 up to 2, n = 2 up to 8, n = 3 up to 18, n = 4 up to 32; the relationship is 2n².
Principal quantum shells are split into subshells labelled s, p and d; elements with more than 57 electrons also have an f subshell.
The energy of electrons in subshells increases in the order s < p < d < f.
The order of subshells overlaps for higher principal quantum shells; the only exception is that the 3d orbital has slightly higher energy than the 4s orbital, so 4s is filled before 3d.

Orbitals

Subshells contain one or more atomic orbitals; orbitals exist at specific energy levels and electrons can only be found at these levels, not in between.
Each atomic orbital can be occupied by a maximum of two electrons.
An s subshell has 1 orbital, a p subshell has 3 orbitals (px, py, pz), a d subshell has 5 orbitals, and an f subshell has 7 orbitals.
The maximum number of electrons in each subshell is: s = 2, p = 6, d = 10, f = 14.
In the ground state, orbitals in the same subshell have the same energy and are said to be degenerate (e.g. px, py and pz have the same energy).
s orbitals are spherical in shape; their size increases with increasing shell number.
p orbitals are dumbbell-shaped; every shell has three p orbitals except n = 1, and they occupy the x, y and z axes, pointing at right angles to each other.
The lobes of p orbitals become larger and longer with increasing shell number.

Ground State and the Aufbau Principle

The ground state is the most stable electronic configuration of an atom, with the lowest amount of energy.
This is achieved by filling the subshells of lowest energy first (1s), known as the Aufbau Principle.
The order of subshells in terms of increasing energy does not follow a regular pattern at n = 3 and higher.
The principal quantum shells increase in energy with increasing principal quantum number (e.g. n = 4 is higher in energy than n = 2).
Following the Aufbau diagram arrows gives the filling order of subshells.

Writing Electron Configurations

The electron configuration gives information about the number of electrons in each shell, subshell and orbital of an atom.
Electrons can be imagined as small spinning charges rotating clockwise or anticlockwise; electrons with the same spin repel each other (spin–pair repulsion).
Hund's rule: electrons fill degenerate orbitals singly first, with parallel spins, to minimise repulsion; they pair only after all orbitals are singly occupied, with opposite spins.
Pauli Exclusion Principle: an orbital holds two electrons with opposite spins only; electrons pair only when no empty orbital of the same energy is available, as pairing costs less energy than jumping to a higher orbital.
There are two formats: full configuration lists all electrons from 1s onward; shorthand configuration uses the nearest noble gas symbol in brackets (e.g. [Ar]) to represent inner electrons.
Ions form when atoms gain or lose electrons: anions (negative) form by adding electrons to the outer shell; cations (positive) form by removing electrons from the outer shell.
For transition metals: fill 4s before 3d when neutral; lose electrons from 4s first, not 3d, when forming ions.
In the Periodic Table, elements are grouped into blocks based on their valence subshell: s-block, p-block, d-block and f-block.

Electron shells and the Periodic Table

Examples and Exceptions

Fe (Z = 26): full configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶; shorthand [Ar] 4s² 3d⁶.
Fe²⁺ ion: electrons removed from 4s before 3d; full configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶; shorthand [Ar] 3d⁶.
Cr is [Ar] 3d⁵ 4s¹ not [Ar] 3d⁴ 4s²; Cu is [Ar] 3d¹⁰ 4s¹ not [Ar] 3d⁹ 4s².
These exceptions occur because promoting an electron from 4s to 3d achieves a half-full or full d-subshell, which is energetically favourable.
Potassium (Z = 19): full 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹; shorthand [Ar] 4s¹.
Calcium (Z = 20): full 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²; shorthand [Ar] 4s².
Gallium (Z = 31): full 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p¹; shorthand [Ar] 3d¹⁰ 4s² 4p¹.
Ca²⁺ ion: loses two 4s electrons; full 1s² 2s² 2p⁶ 3s² 3p⁶; shorthand [Ar], same configuration as argon.

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練習問題

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1.What is the shape of an s orbital?
Easy
- ASpherical
- BDumbbell-shaped
- CTetrahedral
- DLinear
2.How many orbitals are there in a p subshell?
Easy
- A1
- B3
- C5
- D7
3.What is the maximum number of electrons that can occupy the n = 3 energy level?
Medium
- A8
- B18
- C32
- D2
4.Which electron transition would emit radiation of the longest wavelength?
Medium
- An = 4 to n = 2
- Bn = 3 to n = 2
- Cn = 2 to n = 1
- Dn = 5 to n = 1
5.What is the correct sequence for the orbitals shown in an atom of vanadium in order of decreasing energy?
Medium
- A3s > 3p > 4s > 3d
- B4s > 3d > 3s > 3p
- C4s > 3d > 3p > 3s
- D3d > 4s > 3p > 3s
6.Which of the following statements about the electromagnetic spectrum are correct? (select all that apply)
Medium
- AAll electromagnetic waves travel at the same speed in a vacuum.
- BFrequency and wavelength are inversely related.
- CGamma rays have lower energy than radio waves.
- DThe speed of light in a vacuum is 3.00 × 10⁸ m s⁻¹.
- EHigher frequency means longer wavelength.
7.A continuous spectrum contains all colours of visible light with no gaps.
Easy
True or false?
8.In the ground state, the 4s orbital is filled before the 3d orbital.
Easy
True or false?

もっと問題

9.Match each subshell with the number of orbitals it contains.
Medium
- s
- p
- d
- f
- 1
- 3
- 5
- 7
10.Place the following regions of the electromagnetic spectrum in order of increasing frequency.
Medium
- Radio waves
- Infrared
- Visible light
- Ultraviolet
- Gamma rays
11.Which electron transition in the hydrogen atom emits visible light?
Medium
- An = 1 to n = 2
- Bn = 2 to n = 3
- Cn = 2 to n = 1
- Dn = 3 to n = 2
12.Which of the following is the correct full electron configuration for a calcium ion, Ca²⁺?
Easy
- A1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
- B1s² 2s² 2p⁶ 3s² 3p⁶
- C1s² 2s² 2p⁶ 3s² 3p⁶ 3d²
- D1s² 2s² 2p⁶ 3s² 3p⁴
13.Using the Aufbau Principle and Hund's rule, deduce which element below has the greatest number of unpaired electrons in its ground state.
Medium
- AZ = 13
- BZ = 14
- CZ = 15
- DZ = 16
14.There are six unpaired electrons in atoms of element Z. What could element Z be?
Medium
- Asulfur
- Biron
- Ccarbon
- Dchromium
15.Which species produces a half-filled set of p orbitals on losing an electron?
Medium
- ALi⁺
- BF
- CN
- DN⁻
16.Which statement explains why electrons pair up in orbitals before occupying an orbital of a higher energy level?
Medium
- Athe energy from repulsion is greater than the jump to a higher orbital
- Belectrons occupy higher energy orbitals before lower energy orbitals
- Celectrons in lower orbitals have higher energies
- Dthe energy from repulsion is less than the jump to a higher orbital
17.A line emission spectrum occurs when
Medium
- Aelectrons release energy as they move from high to low energy levels
- Belectrons release energy as they move from low to high energy levels
- Celectrons absorb energy as they move from high to low energy levels
- Delectrons absorb energy as they move from low to high energy levels
18.A spectral line that would be found in the visible spectrum of the hydrogen emission spectrum would be
Hard
- An = 1 → n = 2
- Bn = 2 → n = 3
- Cn = 3 → n = 2
- Dn = 3 → n = ∞
19.Which statements about the electromagnetic spectrum are correct? (select all that apply)
Medium
- AAll electromagnetic waves travel at the same speed in a vacuum.
- BFrequency and wavelength are directly proportional.
- CGamma rays have higher energy than radio waves.
- DThe speed of light in a vacuum is 3.00 × 10⁸ m s⁻¹.
- EUltraviolet radiation has a longer wavelength than infrared radiation.
20.Which of the following statements about electron configuration rules are correct? (select all that apply)
Medium
- AThe Aufbau Principle states that subshells of lowest energy are filled first.
- BHund's rule states that electrons pair up in orbitals before occupying empty orbitals of the same energy.
- CThe Pauli Exclusion Principle states that an orbital can hold a maximum of two electrons with opposite spins.
- DIn a p subshell, electrons fill px, py and pz singly before pairing.
- EElectrons with the same spin attract each other, so they occupy the same orbital.
21.The shape of a p orbital is spherical.
Easy
True or false?
22.Match each region of the hydrogen emission spectrum with the electron transition that produces it.
Medium
- Transition from n = ∞ to n = 3
- Transition from n = ∞ to n = 2
- Transition from n = ∞ to n = 1
- Infrared
- Visible
- Ultraviolet
23.Place the following orbitals in order of increasing energy in a multi-electron atom.
Medium
- 1s
- 2s
- 2p
- 3s
- 3p
- 4s
- 3d
24.The diagram shows three orbitals labelled 1, 2 and 3. Orbital 1 is spherical, orbital 2 is dumbbell-shaped along the y-axis, and orbital 3 is dumbbell-shaped along the x-axis. What is the correct label for each orbital?
Medium
- As, p_y and p_x
- Bp_x, p_y and p_z
- Cs, p_x and p_y
- Dp_y, p_x and s
25.What is the electronic configuration of an ion with a single negative charge and atomic number 17?
Medium
- A1s² 2s² 2p⁶ 3s² 3p⁶
- B1s² 2s² 2p⁶ 3s² 3p⁵
- C1s² 2s² 2p⁶ 3s² 3p⁴
- D1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
26.Deduce the correct information about the element tin, Sn (Z = 50).
Medium
- ANumber of occupied main energy levels = 5; number of electrons in the highest main energy level = 4
- BNumber of occupied main energy levels = 4; number of electrons in the highest main energy level = 4
- CNumber of occupied main energy levels = 4; number of electrons in the highest main energy level = 14
- DNumber of occupied main energy levels = 5; number of electrons in the highest main energy level = 14
27.Which statement is true about the spectra shown? Spectrum P is continuous, Q is a line spectrum, R is a line spectrum, and S is a continuous spectrum.
Medium
- AOnly S shows the characteristic pattern of a line emission spectrum
- BAll the lines in R have the same energy
- CQ and S could represent line emission spectra
- DP indicates the element has 4 pairs of electrons at different energy levels
28.The first four lines of the Balmer series of hydrogen have wavelengths: Hα 656 nm (red), Hβ 486 nm (cyan), Hγ 434 nm (blue), Hδ 410 nm (violet). Which statement about these lines is correct?
Hard
- AHα has the lowest frequency and lowest energy
- BHδ has the longest wavelength and lowest energy
- CHα has the highest frequency and highest energy
- DHβ has a higher energy than Hγ
29.The first four lines of the Balmer series of hydrogen have wavelengths: Hα 656 nm, Hβ 486 nm, Hγ 434 nm, Hδ 410 nm. Using c = fλ, determine the ratio of the frequency of Hα to the frequency of Hγ to 2 decimal places.
Hard
- A0.66
- B1.51
- C1.00
- D0.43
30.The diagram shows electron transitions in a hydrogen atom. Using the regions of the electromagnetic spectrum, predict which electron transition is most likely to correspond to the emission of red light.
Hard
- An = 3 to n = 2
- Bn = 2 to n = 1
- Cn = 4 to n = 1
- Dn = 5 to n = 3
31.The diagram shows electron transitions in a hydrogen atom. Predict which electron transition will correspond to the greatest frequency of light emitted.
Hard
- An = ∞ to n = 1
- Bn = 4 to n = 2
- Cn = 3 to n = 2
- Dn = 5 to n = 3
32.The relative atomic mass of rubidium is 85.47. Rubidium has two naturally occurring isotopes, ⁸⁵Rb and ⁸⁷Rb. What is the percentage abundance of ⁸⁵Rb?
Medium
- A76.5%
- B23.5%
- C50.0%
- D85.5%
33.The element chromium has several naturally occurring isotopes: ⁵⁰Cr (4.345%), ⁵²Cr (83.789%), ⁵³Cr (9.501%), ⁵⁴Cr (2.365%). Calculate the relative atomic mass of chromium to two decimal places.
Medium
- A52.06
- B52.00
- C52.50
- D51.94
34.Which statements about the emission spectrum of hydrogen are correct? (select all that apply)
Hard
- AThe lines converge towards the higher energy end of the spectrum
- BThe visible lines correspond to electron transitions ending at n = 2
- CThe spectrum contains all frequencies of visible light
- DThe lines in the ultraviolet region correspond to transitions ending at n = 1
- EThe energy of the emitted light is inversely proportional to the frequency
35.In a multi-electron atom, the 4s orbital is filled before the 3d orbital.
Easy
True or false?
36.The lines in the visible emission spectrum of hydrogen get closer together towards the red end of the spectrum.
Medium
True or false?
37.Match each region of the electromagnetic spectrum with the type of electron transition in the hydrogen atom that produces it.
Medium
- Infrared
- Visible
- Ultraviolet
- Transitions ending at n = 3
- Transitions ending at n = 2
- Transitions ending at n = 1
38.Place the following electron transitions in a hydrogen atom in order of increasing energy of the emitted photon.
Medium
- n = 4 to n = 3
- n = 3 to n = 2
- n = 2 to n = 1
39.A student obtains a line emission spectrum of an unknown element using a discharge tube and a diffraction grating. Which statement best explains why the observed spectrum consists of sharp, discrete lines rather than a continuous band of colours?
Medium
- AElectrons in the atoms can only occupy certain fixed energy levels, so only photons of specific energies are emitted.
- BThe diffraction grating absorbs all wavelengths except a few selected colours.
- CThe discharge tube only contains a single excited atom at any instant.
- DWhite light from the tube is refracted into its component colours by the grating.
40.Which of the following statements about the practical recording of an emission spectrum using a discharge tube and diffraction grating are correct? (select all that apply)
Medium
- AThe discharge tube contains a gas at low pressure.
- BThe diffraction grating separates the emitted light into its component wavelengths.
- CA continuous spectrum is observed if the gas is pure hydrogen.
- DThe lines observed correspond to electron transitions from higher to lower energy levels.
- EThe spectrum is recorded by measuring the wavelengths of the emitted photons.
41.What is the term for the most stable electronic configuration of an atom, which has the lowest amount of energy?
Easy
42.How many orbitals are there in the n = 4 energy level?
Medium
43.Complete the sentence about electron configuration rules.
Easy
The rule that electrons fill degenerate orbitals singly first, with parallel spins, is called ____ rule.
44.The red line of the hydrogen emission spectrum has a wavelength of 656 nm. Using c = fλ and c = 3.00 × 10⁸ m s⁻¹, calculate the frequency of this line in Hz. Give your answer to three significant figures.
Medium
45.An electromagnetic wave has a frequency of 5.00 × 10¹⁴ Hz. Using c = fλ and c = 3.00 × 10⁸ m s⁻¹, calculate its wavelength in nm. Give your answer to three significant figures.
Medium
46.Complete the sentence about the electromagnetic spectrum.
Medium
Frequency and wavelength are ____ related, so a higher frequency means a ____ wavelength.
47.State the term for the most stable electronic configuration of an atom, which has the lowest amount of energy.
Easy
48.Give the name of the principle that states an orbital can hold a maximum of two electrons with opposite spins.
Medium
49.Calculate the relative atomic mass of chromium to two decimal places.
Medium
50.Complete the sentence about electron configurations.
Medium
The ____ Principle states that electrons fill the lowest energy orbitals first, while ____ rule states that electrons occupy degenerate orbitals singly before pairing.
51.The red line of the hydrogen emission spectrum has a wavelength of 656 nm. Using c = fλ and c = 3.00 × 10⁸ m s⁻¹, calculate the frequency of this line in Hz. Give your answer in scientific notation to three significant figures.
Medium
52.The relative atomic mass of rubidium is 85.47. Rubidium has two naturally occurring isotopes, ⁸⁵Rb and ⁸⁷Rb. Calculate the percentage abundance of ⁸⁵Rb.
Medium
53.State what is meant by the term orbital.
Medium
54.Describe the process occurring in an atom to produce a single line on an emission spectrum.
Hard
55.Distinguish between a continuous spectrum and a line spectrum.
Hard
56.Describe the emission spectrum of hydrogen and outline how this spectrum is related to the energy levels in the hydrogen atom.
Hard
57.State the full electron configuration for chromium.
Hard
58.How many orbitals are there in the n = 4 energy level?
Medium
- A18 orbitals
- B16 orbitals
- C15 orbitals
- D17 orbitals
59.The red line of the hydrogen emission spectrum has a wavelength of 656 nm. Using c = fλ and c = 3.00 × 10⁸ m s⁻¹, calculate the frequency of this line in Hz. Give your answer to three significant figures.
Medium
- A548400000000000 Hz
- B502700000000000 Hz
- C457000000000000 Hz
- D411300000000000 Hz
60.An electromagnetic wave has a frequency of 5.00 × 10¹⁴ Hz. Using c = fλ and c = 3.00 × 10⁸ m s⁻¹, calculate its wavelength in nm. Give your answer to three significant figures.
Medium
- A600 nm
- B540 nm
- C720 nm
- D660 nm
61.Calculate the relative atomic mass of chromium to two decimal places.
Medium
- A46.85
- B52.06
- C57.27
- D62.48
62.The red line of the hydrogen emission spectrum has a wavelength of 656 nm. Using c = fλ and c = 3.00 × 10⁸ m s⁻¹, calculate the frequency of this line in Hz. Give your answer in scientific notation to three significant figures.
Medium
- A411300000000000 Hz
- B548400000000000 Hz
- C502700000000000 Hz
- D457000000000000 Hz
63.The relative atomic mass of rubidium is 85.47. Rubidium has two naturally occurring isotopes, ⁸⁵Rb and ⁸⁷Rb. Calculate the percentage abundance of ⁸⁵Rb.
Medium
- A76.5 %
- B91.9 %
- C68.8 %
- D84.2 %

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