When the hydrogen ion concentration [H$$^+$$] changes by a factor of 1000, the value of pH of the solution

The pH of a solution is related to the hydrogen ion concentration by the expression $$pH = -\log_{10}[H^+]$$.

Let the initial hydrogen ion concentration be $$[H^+]_1$$. Then, the initial pH is $$pH_1 = -\log[H^+]_1$$.

If the hydrogen ion concentration increases by a factor of 1000, then the new concentration becomes $$[H^+]_2 = 1000[H^+]_1$$.

The new pH is

$$pH_2 = -\log(1000[H^+]_1) = -(\log1000 + \log[H^+]_1) = -(3 + \log[H^+]_1) = pH_1 - 3.$$

Hence, when the hydrogen ion concentration increases by a factor of 1000, the pH decreases by 3 units.

Similarly, if the hydrogen ion concentration decreases by a factor of 1000, then $$[H^+]_2 = \frac{[H^+]_1}{1000}$$.

The new pH becomes

$$pH_2 = -\log\left(\frac{[H^+]_1}{1000}\right) = -(\log[H^+]_1 - 3) = pH_1 + 3.$$

Therefore, a thousandfold decrease in hydrogen ion concentration increases the pH by 3 units.

Hence, for a thousandfold increase in hydrogen ion concentration, the correct statement is that the pH decreases by 3 units. Therefore, the correct answer is $$\boxed{\text{B}}$$.