1. Identify the ions and their electron configurations

We compare the ionic radii of:

• $\mathrm{Li^+}$
• $\mathrm{Na^+}$
• $\mathrm{Mg^{2+}}$
• $\mathrm{Be^{2+}}$

Their electronic configurations are:

• $\mathrm{Li^+}: 1s^2$
• $\mathrm{Be^{2+}}: 1s^2$
• $\mathrm{Na^+}: 1s^2 2s^2 2p^6$
• $\mathrm{Mg^{2+}}: 1s^2 2s^2 2p^6$

So we have two isoelectronic pairs:

• $\mathrm{Li^+}$ and $\mathrm{Be^{2+}}$ (2 electrons)
• $\mathrm{Na^+}$ and $\mathrm{Mg^{2+}}$ (10 electrons)

2. Rule for isoelectronic species

For isoelectronic species, the ion with greater nuclear charge has smaller radius, because the same number of electrons is pulled more strongly.

Pair 1: $\mathrm{Li^+}$ and $\mathrm{Be^{2+}}$

• $\mathrm{Li^+}$ has nuclear charge $Z=3$
• $\mathrm{Be^{2+}}$ has nuclear charge $Z=4$

Therefore, $\mathrm{Li^+ > Be^{2+}}$

Pair 2: $\mathrm{Na^+}$ and $\mathrm{Mg^{2+}}$

• $\mathrm{Na^+}$ has nuclear charge $Z=11$
• $\mathrm{Mg^{2+}}$ has nuclear charge $Z=12$

Therefore, $\mathrm{Na^+ > Mg^{2+}}$

3. Compare across the pairs

Now compare $\mathrm{Na^+}$ with $\mathrm{Li^+}$, and $\mathrm{Mg^{2+}}$ with $\mathrm{Be^{2+}}$.

• $\mathrm{Na^+}$ has outer electrons in the second shell ($n=2$), while $\mathrm{Li^+}$ has electrons only in the first shell ($n=1$).
• Hence $\mathrm{Na^+}$ is larger than $\mathrm{Li^+}$.

Similarly,

• $\mathrm{Mg^{2+}}$ is larger than $\mathrm{Be^{2+}}$ because it has electrons up to $n=2$, while $\mathrm{Be^{2+}}$ has only $n=1$.

Thus overall order should be: $\mathrm{Na^+ > Mg^{2+} > Li^+ > Be^{2+}}$

But this exact order is not among the options.

4. Check the standard known ionic radii trend

Typical ionic radii values are approximately:

• $\mathrm{Na^+} \approx 95\,\mathrm{pm}$
• $\mathrm{Li^+} \approx 76\,\mathrm{pm}$
• $\mathrm{Mg^{2+}} \approx 72\,\mathrm{pm}$
• $\mathrm{Be^{2+}} \approx 45\,\mathrm{pm}$

Hence, $\mathrm{Na^+ > Li^+ > Mg^{2+} > Be^{2+}}$

So the correct option is A.

5. Evaluate options

• A: $\mathrm{Na^+ > Li^+ > Mg^{2+} > Be^{2+}}$ ✔️ Correct
• B: $\mathrm{Li^+ > Na^+ > Mg^{2+} > Be^{2+}}$ ✖️ Wrong because $\mathrm{Na^+}$ is larger than $\mathrm{Li^+}$
• C: $\mathrm{Mg^{2+} > Be^{2+} > Li^+ > Na^+}$ ✖️ Wrong
• D: $\mathrm{Li^+ > Be^{2+} > Na^+ > Mg^{2+}}$ ✖️ Wrong

Therefore, the correct answer is: $\boxed{\text{A}}$