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ShellsThe arrangement of electrons in an atom is called the electron configurationElectrons are arranged around the nucleus in principal energy levels or principal quantum shellsPrincipal quantum numbers (n) are used to number the energy levels or quantum shellsThe lower the principal quantum number, the closer the shell is to the nucleusSo, the first shell which is the closest to the nucleus is n = 1The higher the principal quantum number, the greater the energy of the shell and the further away from the nucleusEach principal quantum number has a fixed number of electrons it can holdn = 1 : up to 2 electronsn = 2 : up to 8 electronsn = 3 : up to 18 electronsn = 4 : up to 32 electronsSubshellsThe principal quantum shells are split into subshells which are given the letters s, p and dElements with more than 57 electrons also have an f shellThe energy of the electrons in the subshells increases in the order s The order of subshells appears to overlap for the higher principal quantum shells as seen in the diagram below:Electrons are arranged in principal quantum shells, which are numbered by principal quantum numbersOrbitalsSubshells contain one or more atomic orbitalsOrbitals exist at specific energy levels and electrons can only be found at these specific levels, not in between themEach atomic orbital can be occupied by a maximum of two electronsThis means that the number of orbitals in each subshell is as follows:s : one orbital (1 x 2 = total of 2 electrons)p : three orbitals ( 3 x 2 = total of 6 electrons)d : five orbitals (5 x 2 = total of 10 electrons)f : seven orbitals (7 x 2 = total of 14 electrons)The orbitals have specific 3-D shapess orbital shapeThe s orbitals are sphericalThe size of the s orbitals increases with increasing shell numberE.g. the s orbital of the third quantum shell (n = 3) is bigger than the s orbital of the first quantum shell (n = 1)p orbital shapeThe p orbitals have a dumbbell shapeEvery shell has three p orbitals except for the first

Staircase: not only are the stair steps set at specific heights but the height between steps is fixed). Finally, Bohr suggested that the energy of light emitted from electrified hydrogen gas was equal to the energy difference of the electron’s energy states:Elight = hν = ΔEelectronThis means that only certain frequencies (and thus, certain wavelengths) of light are emitted. Figure 8.5 “Bohr’s Model of the Hydrogen Atom” shows a model of the hydrogen atom based on Bohr’s ideas.Figure 8.5 Bohr’s Model of the Hydrogen AtomBohr’s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.Bohr’s ideas were useful but were applied only to the hydrogen atom. However, later researchers generalized Bohr’s ideas into a new theory called quantum mechanics, which explains the behaviour of electrons as if they were acting as a wave, not as particles. Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). Instead, electrons are collected into groups and subgroups that explain much about the chemical behaviour of the atom.In the quantum-mechanical model of an atom, the state of an electron is described by four quantum numbers, not just the one predicted by Bohr. The first quantum number is called the principal quantum number. Represented by n. (n). The principal quantum number largely determines the energy of an electron. Electrons in the same atom that have the same principal quantum number are said to occupy an electron shell of the atom. The principal quantum number can be any nonzero positive integer: 1, 2, 3, 4,….Within a shell, there may be multiple possible values of the next quantum number, the angular momentum quantum number. Represented by ℓ. (ℓ). The ℓ quantum number has a minor effect on the energy of the electron but also affects the spatial distribution of the electron in three-dimensional space—that is, the shape of an electron’s distribution in space. The value of the ℓ quantum number can be any integer between 0 and n − 1:ℓ = 0, 1, 2,…, n − 1Thus, for a given value of n, there are different possible values of ℓ:If n equalsℓ can be1020 or 130, 1, or 240, 1, 2, or 3and so forth. Electrons within a shell that have the same value of ℓ are said to occupy a subshell in the atom. Commonly, instead of referring to the numerical value of ℓ, a letter represents the value of ℓ (to help distinguish it from the principal quantum number):If ℓ equalsThe letter is0s1p2d3fThe

Quantum Number Calculator Principal Quantum Number (n) ? Positive integer: 1, 2, 3, … Azimuthal Quantum Number (l) ? Integer from 0 to n-1 Magnetic Quantum Number (ml) ? Integer from -l to l Spin Quantum Number (ms) ? ±1/2 Understanding the Quantum Number CalculatorThe Quantum Number Calculator is a valuable tool designed to assist users in understanding and calculating the four quantum numbers that describe the unique quantum state of an electron in an atom. These numbers are essential for comprehending the behavior and arrangement of electrons in atoms, which in turn influences the chemical properties of elements.What Are Quantum Numbers?Quantum numbers are numerical values that describe the distinct energy levels and orbitals of electrons within an atom. There are four primary quantum numbers: Principal Quantum Number (n): This number indicates the main energy level or shell of an electron. It's a positive integer starting from 1 and increases as the electron's energy level rises. Azimuthal Quantum Number (l): Also known as the angular momentum quantum number, it determines the shape of the electron's orbital. This number ranges from 0 to (n-1). Magnetic Quantum Number (ml): This number specifies the orientation of the orbital in space relative to the three axes (x, y, and z). It ranges from -l to +l. Spin Quantum Number (ms): It represents the spin direction of the electron, either +1/2 or -1/2. Applications and Benefits of Using the Quantum Number CalculatorOur Quantum Number Calculator aids in easily determining the correct quantum numbers for electrons in various energy levels and orbitals. It's beneficial for students, educators, and researchers who need to quickly verify quantum states during their studies or work.In academic settings, this calculator supports learning by providing instant feedback on quantum number configurations, allowing students to better grasp theoretical concepts. For professionals, the calculator can save time by efficiently generating necessary orbital configurations for more complex analyses.How the Quantum Numbers Are DerivedThe calculation starts with the Principal Quantum Number (n), which is user-defined and must be a positive integer. Based on this value, the possible values for the Azimuthal Quantum Number (l) range from 0 to (n-1). Once l is selected, the Magnetic Quantum Number (ml) can be set within the range of -l to +l. Finally, the Spin Quantum Number (ms) is chosen from the two possible values: +1/2 or -1/2.Each of these quantum numbers provides specific information about the electron's position and behavior within an atom. By following this hierarchical selection process, the calculator ensures that all quantum states are assigned correctly according to quantum mechanical principles.Relevance to Real-World Use CasesUnderstanding quantum numbers is crucial for fields such as quantum chemistry, spectroscopy, and material science. For instance, quantum numbers can help predict atomic behavior in different states, explain spectral lines in emission spectra, and contribute to the design of new materials with specific electronic properties. By using this calculator, users can streamline the process of identifying the correct states and focus more on applying this knowledge to practical scenarios. FAQQ1: What is