Question

The increasing order of the following elements (atomic numbers given) with respect to atomic radius is \[ Eu(63),\quad Ho(67),\quad La(57),\quad Yb(70) \]

• A. \(La \lt Eu \lt Ho \lt Yb\)
• B. \(Yb \lt Ho \lt Eu \lt La\)
• C. \(Yb \lt Ho \lt La \lt Eu\)
• D. \(Ho \lt Yb \lt La \lt Eu\)

Hint:

Lanthanoid contraction: \[ La \gt Ce \gt Pr \gt \cdots \gt Lu \] Atomic radius decreases steadily across the lanthanoid series due to poor shielding by \(4f\)-electrons.

Answer 1

The Correct Option is B

Step 1: Spot the family.
All four elements La, Eu, Ho and Yb belong to the lanthanoid series, so we simply compare their sizes within this one series.

Step 2: Recall the size trend.
As we move across the lanthanoids from left to right, the atomic radius keeps shrinking. This steady shrinking is called the lanthanoid contraction.

Step 3: Why the size drops.
Every new electron goes into a $4f$ orbital. These $4f$ electrons are very poor at shielding the nucleus, so the outer electrons feel a stronger pull and the atom becomes smaller.

Step 4: Arrange by atomic number.
Higher atomic number means later in the series, hence smaller size. The atomic numbers are $La(57)$, $Eu(63)$, $Ho(67)$, $Yb(70)$.

Step 5: Convert to size order.
Smallest atomic number gives the biggest atom. So size order is $La > Eu > Ho > Yb$.

Step 6: Write increasing order.
Turning it around for increasing radius we get $Yb < Ho < Eu < La$.
\[ \boxed{Yb < Ho < Eu < La} \]