Question

which of the following is the correct electron configuration for titanium (ti)?

• $1s^22s^22p^63s^23p^64s^23d^2$
• $1s^22s^22p^63s^23p^63d^4$
• $1s^22s^22p^63s^23p^64s^24p^2$

Explanation:

To determine the correct electron configuration for titanium (Ti, atomic number 22), we follow the Aufbau principle (electrons fill lower - energy orbitals first). The order of filling is \(1s\), \(2s\), \(2p\), \(3s\), \(3p\), \(4s\), \(3d\), etc.

• The first two electrons go into the \(1s\) orbital: \(1s^{2}\).
• Then two electrons fill the \(2s\) orbital: \(2s^{2}\).
• Next, six electrons fill the \(2p\) orbital: \(2p^{6}\).
• After that, two electrons go to the \(3s\) orbital: \(3s^{2}\).
• Then six electrons fill the \(3p\) orbital: \(3p^{6}\).
• The \(4s\) orbital has lower energy than the \(3d\) orbital, so two electrons fill the \(4s\) orbital: \(4s^{2}\).
• Titanium has 22 electrons. After filling the orbitals up to \(4s^{2}\), we have used \(2 + 2+6 + 2+6 + 2=20\) electrons. We need 2 more electrons, which go into the \(3d\) orbital, so \(3d^{2}\).

Now let's analyze the options:

• Option 1: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{2}\) follows the Aufbau principle and accounts for all 22 electrons of Ti.
• Option 2: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{4}\) is incorrect because it skips filling the \(4s\) orbital (which has lower energy than \(3d\) for filling electrons in the case of building up the electron configuration).
• Option 3: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}4p^{2}\) is incorrect because after \(4s\), the next orbitals to fill are \(3d\) (not \(4p\)) for elements in the transition metal group (Ti is a transition metal).

Answer:

A. \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{2}\)