The frequencies of K_α X-rays for various materials are measured....

According to Moseley's law, the frequency $\nu$ of the $K_\alpha$ X-ray is related to the atomic number $Z$ of the material by the equation:

$\sqrt{\nu} = a(Z - b)$

where $a$ and $b$ are positive constants.

Squaring both sides, we get:

$\nu = a^2(Z - b)^2$

This equation represents a parabola opening upwards with its vertex on the positive $Z$-axis at $Z = b$.

From the given figure, curve d is a parabola opening upwards, which matches this relationship. Curves a and c are concave downwards, and curve b is a straight line.

Thus, curve d represents the correct relationship.