Animated Solution for Chemistry - Periodicity in Properties: In the sixth period, the orbitals that are filled are

Imagine the periodic table not just as a chart of elements, but as a magnificent, multi-story quantum hotel. Each period (or row) in the table represents a new floor in this hotel, and the principal quantum number, $n$, tells us exactly which floor we are standing on. When we talk about the sixth period, we are exploring the architecture of the $n=6$ floor.

But electrons aren't just thrown into rooms randomly. They are incredibly picky guests. They always seek out the rooms (orbitals) that cost the least amount of energy. To predict exactly which rooms get filled and in what order, we rely on a master blueprint known as the Aufbau Principle.

Aufbau and the $(n+l)$ Rule

The Aufbau principle states that electrons fill lower-energy atomic orbitals before filling higher-energy ones. But how do we calculate this energy? Enter the famous $(n+l)$ rule (also known as Madelung's rule). The energy of an orbital is directly proportional to the sum of its principal quantum number ($n$) and its azimuthal quantum number ($l$).

For any general period $n$, the sequence of available orbitals follows a beautiful, predictable mathematical rhythm:

This formula is the golden key. It tells us that a period always begins by filling the $s$ orbital of that shell, then dips down into the inner $f$ and $d$ orbitals (if they exist), and finally caps off the period with the $p$ orbital of the outermost shell.

Now, let's bring our specific value of $n=6$ into this master blueprint. We simply substitute $6$ wherever we see an $n$ in our general formula.

First, we start with the $s$ orbital: $6s$

Next, we check for the $f$ orbital by subtracting $2$ from $n$: $(6-2)f⟹4f$

Then, we look for the $d$ orbital by subtracting $1$ from $n$: $(6-1)d⟹5d$

Finally, we close the period with the $p$ orbital: $6p$

Putting it all together, the raw sequence of orbitals available for filling in the sixth period is:

When Energies Clash

While our formula gave us the sequence, true physicists always verify their results. Let's calculate the exact $(n+l)$ values for these orbitals to ensure they are strictly increasing in energy. Remember the values for $l$: $s=0$, $p=1$, $d=2$, $f=3$.

For the $6s$ orbital: $n+l=6+0=6$

For the $4f$ orbital: $n+l=4+3=7$

For the $5d$ orbital: $n+l=5+2=7$

For the $6p$ orbital: $n+l=6+1=7$

Notice something fascinating? The $4f$, $5d$, and $6p$ orbitals all have the exact same energy score of $7$! When the universe encounters a tie like this, it uses a simple, elegant tie-breaker: the orbital with the lower principal quantum number ($n$) has slightly lower energy and gets filled first.

Comparing our tied orbitals: $n=4$ ($4f$) is lower than $n=5$ ($5d$), which is lower than $n=6$ ($6p$).

Therefore, the strict energy ordering is indeed $4f<5d<6p$. Our derived sequence is absolutely flawless!

By combining the general filling formula with the rigorous verification of the $(n+l)$ rule, we have successfully mapped out the electron journey for the sixth period. The electrons will first occupy the $6s$ orbital, then dive deep into the $4f$ orbital, move up to the $5d$ orbital, and finally settle in the $6p$ orbital.

Matching this with our given options, we can confidently declare that the correct sequence is $6s,4f,5d,6p$. The quantum hotel is fully booked, and every electron is exactly where it belongs!