Question

An element with atomic number \( Z = 11 \) emits \( K_{\alpha} \)-X-ray of wavelength \( \lambda \). The atomic number which emits \( K_{\alpha} \)-X-ray of wavelength \( 4\lambda \) is

• A. 4
• B. 6
• C. 11
• D. 44

Hint:

The wavelength of X-rays is inversely proportional to the square of the atomic number. This is known as Moseley's law.

Answer 1

The Correct Option is B

Step 1: Understanding the relationship.
The wavelength of \( K_{\alpha} \)-X-ray emitted by an element is inversely proportional to the square of its atomic number. Using the relationship \( \lambda \propto \frac{1}{Z^2} \), we can solve for the atomic number emitting a wavelength of \( 4\lambda \).

Step 2: Calculations.
Since \( Z_1 = 11 \) and the wavelength changes by a factor of 4, we find the new atomic number is 6.