Using Dobereiner's law of triads, the missing number is $$ \frac{\mathrm{Li}}{7}, \frac{\mathrm{Na}}{20}, \frac{\mathrm{~K}}{20} $$.

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To solve the problem using Dobereiner's law of triads, we need to understand that this law states that in a triad of elements, the atomic mass of the middle element is approximately equal to the average of the atomic masses of the other two elements.

Given the triad:
- $$ \frac{\mathrm{Li}}{7} $$
- $$ \frac{\mathrm{Na}}{20} $$
- $$ \frac{\mathrm{K}}{20} $$

We can denote the atomic masses as follows:
- Let $$ a = \frac{\mathrm{Li}}{7} $$
- Let $$ b = \frac{\mathrm{Na}}{20} $$
- Let $$ c = \frac{\mathrm{K}}{20} $$

According to Dobereiner's law, we have:
$$
b \approx \frac{a + c}{2}
$$

Now, we can substitute the values into the equation:
$$
\frac{\mathrm{Na}}{20} \approx \frac{\frac{\mathrm{Li}}{7} + \frac{\mathrm{K}}{20}}{2}
$$

To find the missing number, we need to solve for $$ \mathrm{Na} $$ in terms of $$ \mathrm{Li} $$ and $$ \mathrm{K} $$.

Let's rearrange the equation:
$$
2 \cdot \frac{\mathrm{Na}}{20} \approx \frac{\mathrm{Li}}{7} + \frac{\mathrm{K}}{20}
$$
$$
\frac{\mathrm{Na}}{10} \approx \frac{\mathrm{Li}}{7} + \frac{\mathrm{K}}{20}
$$

Now, we can multiply through by 10 to eliminate the fraction:
$$
\mathrm{Na} \approx 10 \left( \frac{\mathrm{Li}}{7} + \frac{\mathrm{K}}{20} \right)
$$

Next, we need to find a common denominator to combine the terms on the right side. The least common multiple of 7 and 20 is 140. Thus, we can rewrite the equation as:
$$
\mathrm{Na} \approx 10 \left( \frac{20 \cdot \mathrm{Li}}{140} + \frac{7 \cdot \mathrm{K}}{140} \right)
$$
$$
\mathrm{Na} \approx 10 \cdot \frac{20 \cdot \mathrm{Li} + 7 \cdot \mathrm{K}}{140}
$$
$$
\mathrm{Na} \approx \frac{10(20 \cdot \mathrm{Li} + 7 \cdot \mathrm{K})}{140}
$$
$$
\mathrm{Na} \approx \frac{20 \cdot \mathrm{Li} + 7 \cdot \mathrm{K}}{14}
$$

Thus, the missing number $$ \mathrm{Na} $$ can be expressed as:
$$
\mathrm{Na} = \frac{20 \cdot \mathrm{Li} + 7 \cdot \mathrm{K}}{14}
$$

This gives us the relationship between the atomic masses of lithium, sodium, and potassium according to Dobereiner's law of triads.
The missing number $$ \mathrm{Na} $$ is calculated as $$ \frac{20 \cdot \mathrm{Li} + 7 \cdot \mathrm{K}}{14} $$.

Using Dobereiner's law of triads, the missing number is \( \frac{\mathrm{Li}}{7}, \frac{\mathrm{Na}}{20}, \frac{\mathrm{~K}}{20} \).

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