To determine if an ion has a noble gas configuration, we examine its electron configuration and compare it with that of a nearby noble gas:
- Sr²⁺ (\(Z = 38\)) loses two electrons, resulting in the electron configuration \([Kr]\), which matches the noble gas krypton.
- Cs⁺ (\(Z = 55\)) loses one electron, resulting in the electron configuration \([Xe]\), matching xenon.
- La³⁺ (\(Z = 57\)) loses three electrons, resulting in the electron configuration \([Xe]\), also matching xenon.
- Yb²⁺ (\(Z = 70\)) loses two electrons, resulting in the electron configuration \([Xe]\), matching xenon.
On the other hand:
- Pb²⁺ does not match any noble gas configuration due to its partially filled \(d\)-orbitals.
- Fe²⁺ does not match a noble gas configuration either, as it retains electrons in the \(d\)-orbital.
Thus, only *Sr²⁺, Cs⁺, La³⁺, and Yb²⁺ have noble gas configurations, totaling four ions.
The Correct answer is: 2
If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1) is equal to:
If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to: