The number of s-electrons present in an ion with 55 protons in its unipositive state is
To count s-electrons, include all electrons in the s-subshells up to the element’s configuration.
The element with 55 protons is cesium (Cs), and its atomic number is Z = 55. The electronic configuration of neutral Cs is:
\(Cs : [Xe] 6s ^1\)
For the unipositive ion Cs+, it loses the single 6s electron, and the configuration becomes:
\(Cs^+: [Xe]\)
Now count the total number of s-electrons in\( Cs^+:\)
• \(1s^2, 2s^2, 3s^2, 4s^2, 5s^2\) contribute \(2 × 5 = 10\) s-electrons.
Thus, the number of s-electrons is 10.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: