Three metals give these values of √(ν) for their strongest X-ray line: calcium (Z = 20), 9.46 ×…

Step 1. Slope. $\dfrac{1.394 \times 10^{9} - 9.46 \times 10^{8}}{29 - 20} = \dfrac{4.48 \times 10^{8}}{9} = 4.98 \times 10^{7}\ \text{Hz}^{1/2}$ for each unit of $Z$.

Step 2. From calcium. $\dfrac{1.096 \times 10^{9} - 9.46 \times 10^{8}}{4.98 \times 10^{7}} = \dfrac{1.50 \times 10^{8}}{4.98 \times 10^{7}} = 3.0$.

Step 3. The element. $Z = 20 + 3 = 23$. It is vanadium.