Ask a New Question
Menu

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 find the specific electron configuration and the name of the element based on the provided quantum numbers, we can analyze each quantum number:

  1. Principal Quantum Number (n): This quantum number indicates the energy level of the electron. Here, \( n = 5 \) means the electron is in the 5th energy level.

  2. Azimuthal Quantum Number (l): The azimuthal quantum number \( l \) determines the shape (or the subshell) of the orbital. With \( l = 2 \), this corresponds to the d subshell.

  3. Magnetic Quantum Number (ml): This quantum number indicates the orientation of the orbital. For \( l = 2 \), the possible values of \( ml \) range from -2 to 2. Here, \( ml = -1 \) indicates one specific d orbital.

  4. Spin Quantum Number (ms): The spin quantum number indicates the spin of the electron, where \( ms = -1/2 \) means the electron is spin-down.

Based on these quantum numbers, the electron characterized has its last filled electron in a 5d orbital.

a. Electron Configuration

To determine the full electron configuration, we need to consider the element's position in the periodic table based on its electron configuration up to the 5d subshell.

  • The 5th energy level begins filling with the 5s subshell, followed by the 4d, and then the 5d subshells.
  • The complete filling order generally is: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} \) followed by the electrons in the 5d subshell.

The last electron described by your quantum numbers (n=5, l=2, ml=-1, ms=-1/2) is one of those in the 5d subshell.

Just before reaching the 5d subshell, maximum of ten electrons can be held in the previous subshells, and the elements filling this 5d subshell are those in the d-block of the 5th period (which include the elements from Dubnium, atomic number 105, onward).

b. Name of the Element

The element that corresponds to having an electron configuration ending in \( 5d^{1} \) would be Rutherfordium (Rf), which is atomic number 104 and has the electron configuration:

\[ [Rn] 5f^{14} 6d^{2} 7s^{2} \]

However, the last electron in your case corresponds to \( 5d^{x} \). Given the nature of the question and the quantum numbers, the focus would be either on Zinc (Zn) which is \( [Ar] 4s^2 3d^{10} \) for fully filled orbital before entering 5d, but based on the specified quantum number we are essentially indicating \( 5d^{1} \).

Conclusion

So, summarizing:

  • The specific electron configuration would be \( [Xe] 6s^{2} 4f^{14} 5d^{x} \).
  • The element represented by these quantum numbers can be assumed to be Rutherfordium (Rf).
I thought it was Platinum?

I apologize for any confusion. Let's clarify the situation regarding the electron configuration based on the quantum numbers you provided.

Given Quantum Numbers:

  • \( n = 5 \)
  • \( l = 2 \)
  • \( m_l = -1 \)
  • \( m_s = -\frac{1}{2} \)

Analyzing the Quantum Numbers

  1. Principal Quantum Number \( n = 5 \): This indicates that the electron is in the 5th energy level.
  2. Azimuthal Quantum Number \( l = 2 \): This corresponds to the d subshell (l = 2 corresponds to d).
  3. Magnetic Quantum Number \( m_l = -1 \): This suggests the electron is in one of the 5d orbitals (the d subshell can house 5 orbitals: -2, -1, 0, +1, +2).
  4. Spin Quantum Number \( m_s = -\frac{1}{2} \): Indicates the electron has a spin in the downward direction.

Thus, the specified quantum numbers indicate an electron in a \( 5d \) orbital, and specifically, it pertains to a configuration where the last electron entered would be in the 5d subshell.

Electron Configuration

The elements that fill the 5d subshell (5th period d-block elements) include:

  • Zirconium (Zr): \( [Kr] 5s^2 4d^2 \)
  • Hafnium (Hf): \( [Xe] 6s^2 4f^{14} 5d^2 \)
  • Rutherfordium (Rf): \( [Rn] 5f^{14} 6d^2 7s^2 \) (although this is a synthetic element with no stable isotopes)

If you are considering Platinum specifically, its complete electron configuration is:

  • Platinum (Pt): \( [Xe] 6s^2 4f^{14} 5d^9 \)

Conclusion

Given the quantum numbers you provided, they correspond more to an element that has electrons being filled in the 5d subshell.

Thus, with an electron configuration indicative of \( 5d^1 \), this would not point to Platinum specifically, as:

  • Platinum has the configuration \( [Xe] 6s^2 4f^{14} 5d^9 \).

However, if you meant that Platinum is among elements represented in a typical context for \( d \)-block elements, you're correct—it occupies that field in the periodic table.

If there was a misunderstanding about the specific quantum numbers meant for Platinum's configuration:

  • If you were referencing a filled \( 5d^{10} \) (for elements like Gold, Mercury, etc.), then, yes, elements like Gold would align more closely with filled configurations in the same period. Give you the quantum number set again, we might further refine it if required.

If you meant Platinum deal with the last filled quantum number arrangements dealing with electrons being added in the \( d \) subshell, it’s a valid inference but just requires clarification on context. Thank you for your understanding!