Question

Given below are two statements about x-ray spectra of elements:

Statement (i): A plot of $\sqrt{v}$ (v = frequency of x-ray emitted) vs atomic mass is a straight line.

Statement (ii): A plot of v (v = frequency of x-ray emitted) vs atomic number is straight line.

In the light of the above statements choose the correct answer from the options given below:

• A. Statement (i) is true but statement (ii) is false
• B. Statement (i) is false but statement (ii) is true
• C. Statement (i) and statement (ii) are false
• D. Statement (i) and statement (ii) are true

Answer 1

Answer: (C)

Both statements are false.

Answer 2

Moseley's law is given by

$$\sqrt{\nu} \propto (Z - \sigma),$$

where $Z$ is the atomic number and $\sigma$ is the screening constant.

• Statement (i): The law relates $\sqrt{\nu}$ with $Z$ (not atomic mass). Hence, a plot of $\sqrt{\nu}$ vs atomic mass will not be a straight line.

• Statement (ii): Since $\sqrt{\nu}$ is linear in $Z$, $\nu$ will be proportional to $(Z-\sigma)^2$. Thus, a plot of $\nu$ vs $Z$ will be quadratic, not linear.