Question

What is the highest value of \(n\) for the electrons in these atoms? (a) \(\overline{\mathrm{Co}}\) (b) As (c) \(\overline{\mathrm{Sr}}\) (d) \(\overline{\mathrm{Po}}\)

Short answer

The highest values of the principal quantum number (n) for the given elements are: (a) Cobalt (Co): \(n = 4\) (b) Arsenic (As): \(n = 4\) (c) Strontium (Sr): \(n = 5\) (d) Polonium (Po): \(n = 6\)

Step-by-step solution

(a) Find the electron configuration for Co

Co is Cobalt and has an atomic number of 27. Using the periodic table, we can determine Co's electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\]

(a) Determine the highest value of n for Co

The electron configuration of Cobalt reveals that the period with the highest principal quantum number (n) is the 4th period: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\). Therefore, the highest value of n for Cobalt (Co) is 4.

(b) Find the electron configuration for As

As is Arsenic and has an atomic number of 33. Using the periodic table, we can determine As's electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3\]

(b) Determine the highest value of n for As

The electron configuration of Arsenic reveals that the period with the highest principal quantum number (n) is the 4th period: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3\). Therefore, the highest value of n for Arsenic (As) is 4.

(c) Find the electron configuration for Sr

Sr is Strontium and has an atomic number of 38. Using the periodic table, we can determine Sr's electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2\]

(c) Determine the highest value of n for Sr

The electron configuration of Strontium reveals that the period with the highest principal quantum number (n) is the 5th period: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2\). Therefore, the highest value of n for Strontium (Sr) is 5.

(d) Find the electron configuration for Po

Po is Polonium and has an atomic number of 84. Using the periodic table, we can determine Po's electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^4\]

(d) Determine the highest value of n for Po

The electron configuration of Polonium reveals that the period with the highest principal quantum number (n) is the 6th period: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^4\). Therefore, the highest value of n for Polonium (Po) is 6.

Key concepts

Periodic Table

The periodic table is an essential tool in chemistry that organizes all the known elements in an informative way. It is structured in rows and columns, with each element strategically placed according to its atomic number, electron configuration, and recurring chemical properties. Each row corresponds to a period in the periodic table, starting with a principal quantum number (n) that increases as you move down the rows.

• Atomic Number: The number of protons in an atom's nucleus, which determines the element's identity.
• Periods and Groups: Rows are known as periods, and columns are called groups. Elements in the same group have similar chemical properties.
• Electron Configuration: The distribution of electrons across different shells and subshells in an element.

The arrangement helps chemists and students predict how elements might behave in chemical reactions. By using the periodic table, one can easily identify the electron configuration for any element, such as Cobalt or Strontium, and accordingly determine properties like the highest value of n.

Principal Quantum Number

In quantum mechanics, the principal quantum number, represented as \( n \), is a vital concept. It defines the principal electron shell or energy level that an electron occupies in an atom. The higher the value of \( n \), the farther the electron is from the nucleus and the higher its energy level.

• Values of \( n \): These are positive integers (1, 2, 3,...) starting from one and increasing as you go up the periods in the periodic table.
• Electron Shells: Shells are labeled as K, L, M, N, etc., corresponding to \( n \) values of 1, 2, 3, 4, etc.
• Energy Levels: Higher \( n \) values imply higher energy levels and larger atomic sizes.

The principal quantum number is elemental in understanding electron arrangements in atoms. For example, when examining Polonium (Po), the highest \( n \) is 6, indicating electrons on the sixth energy level.

Highest Value of n

To determine the highest value of \( n \) for an atom's electrons, one examines its electron configuration. The highest principal quantum number, \( n \), dictates the outermost or valence shell, which plays a key role in chemical bonding and reactions.

• Outer Electron Shell: Where the highest-numbered \( n \) electrons reside.
• Chemical Properties: Elements with the same highest \( n \) value share similar chemical properties.
• Electron Configuration: Look at the highest number in the electron configuration to find the greatest \( n \).

For instance, Strontium (Sr) has an electron configuration ending in \( 5s^2 \), giving it a highest \( n \) of 5, which influences its reactivity and interaction with other elements.

Atomic Number

The atomic number is a fundamental characteristic of an element, representing the total number of protons in the nucleus of an atom. It uniquely identifies each element and determines its position in the periodic table.

• Unique Identifier: No two elements can share the same atomic number.
• Determines Electron Configuration: As protons equal electrons in neutral atoms, the atomic number also tells us the electron structure.
• Defines Element Identity: Changing the atomic number transforms one element into another.

For example, Arsenic (As) has an atomic number of 33, meaning it has 33 protons and, in its neutral state, 33 electrons. This atomic number helps dictate its electron configuration, which in turn helps to figure out properties like the highest principal quantum number (\( n \)).