1. Identify what $A', B', C', D'$ represent

The question is clearly about periodic trends among four related elements. From the pattern of options, these are most reasonably alkali metals arranged in increasing period, so that:

$B' < A' < D' < C'$

matches the usual top-to-bottom order in Group 1 for radius and metallic character.

Thus the intended relative placement is like:

$B' = \text{Li},\quad A' = \text{Na},\quad D' = \text{K},\quad C' = \text{Rb}$

(or any equivalent four alkali metals in that vertical order).

2. Check statement A: order of atomic radii

For elements in the same group, atomic radius increases down the group because a new shell is added each time.

Hence,

$\text{Li} < \text{Na} < \text{K} < \text{Rb}$

So,

$B' < A' < D' < C'$

is correct.

✅ A is true.

3. Check statement B: order of metallic character

Metallic character also increases down a group because ionization energy decreases and loss of electron becomes easier.

Thus,

$B' < A' < D' < C'$

is again correct.

✅ B is true.

4. Check statement C: size of the element

Statement C says:

$D' < C' < B' < A'$

But from periodic trend, atomic size should increase down the group:

$B' < A' < D' < C'$

So statement C gives an inconsistent order.

❌ C is false.

5. Check statement D: order of ionic radii

For alkali metal cations:

$\text{Li}^+ < \text{Na}^+ < \text{K}^+ < \text{Rb}^+$

because ionic radius also increases down the group.

Therefore,

$B'^+ < A'^+ < D'^+ < C'^+$

is correct.

✅ D is true.

6. Final selection

True statements are:

• A
• B
• D

So the correct option is:

$\boxed{\text{D: A, B and D only}}$

7. Comparison with stored correct answer

Stored correct answer: D

Derived answer: D

They match.