Question

In a Compton scattering experiment, the wavelength of incident X-rays is 0.500 Å. If the Compton wavelength \(\lambda_C = 0.024\, \text{Å}\), the value of the longest wavelength possible for the scattered X-ray is ............... Å. (Specify up to 3 decimal places.)

Hint:

The maximum wavelength shift in Compton scattering occurs when the photon is scattered backward (\(\theta = 180^\circ\)).

Answer 1

Correct Answer: 0.548

Step 1: Use Compton shift formula.
\[ \Delta \lambda = \lambda_C (1 - \cos\theta) \] The longest wavelength occurs at \(\theta = 180^\circ\): \[ \Delta \lambda_{\max} = 2\lambda_C = 2(0.024) = 0.048\, \text{Å} \] \[ \lambda'_{\max} = \lambda + \Delta\lambda = 0.500 + 0.048 = 0.548\, \text{Å} \]

Step 2: Conclusion.
Hence, the longest possible scattered wavelength = 0.548 Å.