Question

Given below are two statements about X-ray spectra of elements:
Statement (I):A plot of \(\sqrt {v}\) (v=frequency of X-rays emitted) vs atomic mass is a straight line.
Statement (II): A plot of v (v=frequency of X-rays emitted)} vs atomic number is a straight line.

• A. Statement I is true but Statement II is false
• B. Both Statement I and Statement II are true
• C. Both Statement I and Statement II are false
• D. Statement I is false but Statement II is true

Hint:

X-ray emission frequency typically follows Moseley's law, which indicates a square root dependence on the atomic number.

Answer 1

The Correct Option is C

Let's analyze both statements provided regarding X-ray spectra of elements. 

1. Understanding Statement I: "A plot of \(\sqrt {v}\) (where \(v\) is the frequency of X-rays emitted) vs atomic mass is a straight line."
   • The relation of frequency of emitted X-rays is better understood through Moseley's law, which states that the square root of the frequency of the characteristic X-ray is proportional to the atomic number (Z) of the element and not the atomic mass.
   • Moseley’s law is mathematically represented as \(\sqrt{v} = a(Z - b)\), where \(a\) and \(b\) are constants. This shows a linear relationship between \(\sqrt{v}\) and \(Z\), not atomic mass.
   • Thus, Statement I is false because the correct plot should involve atomic number, not atomic mass.
2. Understanding Statement II: "A plot of \(v\) (where \(v\) is the frequency of X-rays emitted) vs atomic number is a straight line."
   • According to Moseley’s law, the plot involving the square root of the frequency is what exhibits linearity with the atomic number, not the frequency itself.
   • A direct plot of frequency \(v\) vs \(Z\) is not linear, as the relationship involves the square root of frequency.
   • Thus, Statement II is also false.

After careful examination of both statements based on Moseley’s law, both statements are found to be false. Therefore, the correct answer is:

Both Statement I and Statement II are false.

Answer 2

Statement (I): A plot of frequency \( \nu \) vs atomic mass is not a straight line. The relationship between atomic mass and X-ray emission frequency is not linear. This statement is false.
- Statement (II): A plot of frequency \( \nu \) vs atomic number is also not a straight line. The frequency of X-rays emitted generally follows Moseley's law, which is a square root function of the atomic number, not a linear function. This statement is false.
Thus, both statements are false.