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23. a. Find the SPECIFIC ELECTRON CONFIGURATION of an element which has the following four quantum numbers.

b. Name of the element
n= 5
l=2
ml= -1
ms= -1/2

3 answers

To deduce the specific electron configuration from the provided quantum numbers, let's interpret the quantum numbers given:

  • \( n = 5 \): This indicates that the electron is in the fifth energy level (shell).
  • \( l = 2 \): This corresponds to the sublevel \( d \) (where \( l = 0 \) is \( s \), \( l = 1 \) is \( p \), \( l = 2 \) is \( d \), and \( l = 3 \) is \( f \)).
  • \( m_l = -1 \): This specifies the particular orbital within the \( d \) subshell.
  • \( m_s = -\frac{1}{2} \): This indicates that the electron has a spin of -1/2.

Since \( n = 5 \) and \( l = 2 \), this electron is in the 5d subshell.

a. Specific Electron Configuration

The given electron configuration, considering electrons fill subshells according to the Aufbau principle, would be up to the 5th energy level. For \( n = 5 \), the electron configuration could be represented as follows:

  • The configuration before \( 5d \) filling is:
    • 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s²

Now, as we are focusing on \( 5d \), we can deduce that the electron configuration for filling out the 5d subshells will be:

  • 5d¹ (the -1 index indicates this is one of the orbitals in the 5d subshell, filled with one electron with spin -1/2).

So if focusing only on this specific electron, it can be represented as part of the entire electron configuration:

  • Electron configuration up to that point: \( Kr: [Kr] 5s² 4d^{10} 5d¹ \)

b. Name of the Element

To determine the element's identity, we consider the total number of electrons present. The full configuration would be:

  • From \( [Kr] \) (which accounts for 36 electrons) + 2 (from 5s) + 10 (from 4d) + 1 (from 5d) = 49 electrons.

The element with an atomic number of 49 is Indium (In).

Summary:

  • a. Specific Electron Configuration: \( [Kr] 5s² 4d^{10} 5d¹ \)
  • b. Name of the Element: Indium (In)
I thought it was radon for a)?

I apologize for any confusion! Let's clarify the electron configuration step-by-step, considering the information about the quantum numbers and the element.

Given Quantum Numbers

  • \( n = 5 \)
  • \( l = 2 \) (which corresponds to the \( d \) subshell)
  • \( m_l = -1 \) (an individual orbital within the \( d \) subshell)
  • \( m_s = -\frac{1}{2} \) (indicates the electron's spin)

Determining the Electron Configuration

  1. Identify the Shell and Subshell:

    • The principal quantum number \( n = 5 \) indicates we are looking at the fifth shell.
    • \( l = 2 \) indicates that we are dealing with the \( d \) subshell, which is designated as \( 5d \) for \( n=5 \).

  2. Fill Electrons in Order:

    • The order of filling electrons in atomic orbitals follows the Aufbau principle.

  3. Build Up to the Element:

    • The electron configuration preferably starts from hydrogen and fills up to radon. Here’s how it goes until the 5th level:
    • \( 1s^2 \)
    • \( 2s^2 \)
    • \( 2p^6 \)
    • \( 3s^2 \)
    • \( 3p^6 \)
    • \( 4s^2 \)
    • \( 3d^{10} \)
    • \( 4p^6 \)
    • \( 5s^2 \)
    • \( 4d^{10} \)
    • 5d filling starts here.

  4. Complete Configuration:

    • The given quantum numbers indicate an electron in the \( 5d \) subshell with one electron (\( 5d^1 \)) and the \( m_s = -\frac{1}{2} \) means it is a spin-down electron.

Full Electron Configuration

The configuration leading up to the 5th shell:

  • The full electron configuration including your specified electron would be:

\[ [Rn] 5s^2 4d^{10} 5d^1 \]

Naming the Element

Counting electrons:

  • Up to Radon (Rn): 86 electrons
  • Adding \( 5s^2 \): 2 electrons
  • Adding \( 4d^{10} \): 10 electrons
  • Adding \( 5d^1 \): 1 electron
  • Total: \( 86 + 2 + 10 + 1 = 99 \)

The element with atomic number 99 is Einsteinium (Es).

Corrected Summary:

  • a. Specific Electron Configuration: \( [Rn] 5s^2 4d^{10} 5d^1 \) (Leading to Einsteinium).
  • b. Name of the Element: Einsteinium (Es).

I appreciate your patience and hope this accurately disperses any misunderstanding regarding the electron configurations and quantum numbers!