The wavelength of `K_(alpha)` X-ray line for an element is `0.42Å` . Find the wavelength of `K_(beta)` line emitted by the same element.

Explanation

To find the wavelength of the K-beta X-ray line emitted by the same element, we can use the relationship between the wavelengths of the K-alpha and K-beta lines based on their transitions in the atomic energy levels. Here’s a step-by-step solution:

### Step 1: Understand the transitions
- The K-alpha (Kα) line corresponds to the transition from the second energy level (n=2) to the first energy level (n=1).
- The K-beta (Kβ) line corresponds to the transition from the third energy level (n=3) to the first energy level (n=1).

### Step 2: Write the formula for wave numbers
The wave number (ν) is related to the wavelength (λ) by the formula:
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