Hydrogen ion concentration in mol/L in a solution of pH $$= 5.4$$ will be

The relation between hydrogen ion concentration and pH is given by
$$\text{pH} = -\log_{10}\!\bigl[H^{+}\bigr]$$

Re-arranging for $$\bigl[H^{+}\bigr]$$ gives the antilogarithm formula
$$\bigl[H^{+}\bigr] = 10^{-\text{pH}}$$

For the given solution, $$\text{pH} = 5.4$$, so
$$\bigl[H^{+}\bigr] = 10^{-5.4}$$

Write $$10^{-5.4}$$ as $$10^{-5}\times 10^{-0.4}$$:
$$10^{-5.4}=10^{-5}\times 10^{-0.4}$$

The value of $$10^{-0.4}$$ is the reciprocal of $$10^{0.4}$$. Using the common‐log table (or the fact that $$10^{0.4} \approx 2.51$$):
$$10^{-0.4} \approx \frac{1}{2.51} \approx 0.398$$

Hence
$$10^{-5.4}\approx 10^{-5}\times 0.398 = 3.98\times 10^{-6}$$

Therefore, the hydrogen ion concentration is $$3.98 \times 10^{-6}\ \text{mol L}^{-1}$$.

Option D which is: $$3.98 \times 10^{-6}$$