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Q4.34:
Write the electronic configurations of the elements with the atomic numbers 61, 91, 101, and 109.

Solution :

Step 1: Theoretical Framework for Electronic Configuration

The electronic configuration of elements is governed by the Aufbau Principle (filling orbitals in increasing order of energy), the Pauli Exclusion Principle, and Hund’s Rule of Maximum Multiplicity. For elements beyond Z = 57, we utilize the nearest noble gas core and fill the $4f$, $5d$, $6s$, $6p$, $5f$, $6d$, and $7s$ orbitals sequentially.

Step 2: Configuration for Atomic Number 61 (Promethium, Pm)

Promethium is a member of the lanthanide series ($4f$ block). The nearest noble gas is Xenon ($Xe$, $Z=54$).

  • Remaining electrons: $61 - 54 = 7$.
  • Distribution: The $6s$ orbital fills first, followed by the $4f$ orbital.
  • Configuration: $[Xe] \, 4f^5 \, 6s^2$ [Per the Aufbau filling order for lanthanides].

Step 3: Configuration for Atomic Number 91 (Protactinium, Pa)

Protactinium is an actinide ($5f$ block). The nearest noble gas is Radon ($Rn$, $Z=86$).

  • Remaining electrons: $91 - 86 = 5$.
  • Distribution: Actinides follow the general pattern where electrons occupy the $5f$, $6d$, and $7s$ subshells. For $Pa$, the configuration is $[Rn] \, 5f^2 \, 6d^1 \, 7s^2$.

Step 4: Configuration for Atomic Number 101 (Mendelevium, Md)

Mendelevium is an actinide. The noble gas core is Radon ($Z=86$).

  • Remaining electrons: $101 - 86 = 15$.
  • Distribution: Following the filling of the $5f$ shell, we have $13$ electrons in $5f$ and $2$ in $7s$.
  • Configuration: $[Rn] \, 5f^{13} \, 7s^2$ [Note: The $5f$ orbital is filled preferentially before the $6d$ for late actinides].

Step 5: Configuration for Atomic Number 109 (Meitnerium, Mt)

Meitnerium is a transition metal in the $6d$ series. The noble gas core is Radon ($Z=86$).

  • Remaining electrons: $109 - 86 = 23$.
  • Distribution: The subshells fill as $5f^{14} \, 6d^7 \, 7s^2$.
  • Configuration: $[Rn] \, 5f^{14} \, 6d^7 \, 7s^2$.

Summary Table of Electronic Configurations

Atomic Number (Z) Element Electronic Configuration
61 Promethium (Pm) $[Xe] \, 4f^5 \, 6s^2$
91 Protactinium (Pa) $[Rn] \, 5f^2 \, 6d^1 \, 7s^2$
101 Mendelevium (Md) $[Rn] \, 5f^{13} \, 7s^2$
109 Meitnerium (Mt) $[Rn] \, 5f^{14} \, 6d^7 \, 7s^2$

Final Solution: The electronic configurations are: Pm ($Z=61$): $[Xe] 4f^5 6s^2$; Pa ($Z=91$): $[Rn] 5f^2 6d^1 7s^2$; Md ($Z=101$): $[Rn] 5f^{13} 7s^2$; Mt ($Z=109$): $[Rn] 5f^{14} 6d^7 7s^2$.


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