Statement-1 : In X-rays diffraction, the wavelength of the scattered X-ray is same as that of the incident wavelength .
Statement-2 : The compton wavelength for scattering of X-rays by bound atoms is very small

Options

A. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To analyze the given statements, we will evaluate each one step by step.

### Step 1: Evaluate Statement 1
**Statement 1:** In X-ray diffraction, the wavelength of the scattered X-ray is the same as that of the incident wavelength.

- **Explanation:** In X-ray diffraction, when X-rays interact with a crystal lattice, they can be scattered. The phenomenon of diffraction involves constructive and destructive interference of waves. However, the key point is that in diffraction, the wavelength of the scattered X-rays can change due to the interaction with the crystal structure. Therefore, the wavelength of the scattered X-ray is not necessarily the same as that of the incident wavelength.

- **Conclusion:** Statement 1 is **false**.

### Step 2: Evaluate Statement 2
**Statement 2:** The Compton wavelength for scattering of X-rays by bound atoms is very small.

- **Explanation:** The Compton wavelength is defined as the wavelength associated with a particle (usually an electron) when it scatters a photon (like an X-ray). The Compton effect describes how the wavelength of the photon changes when it scatters off a charged particle. The formula for Compton wavelength is given by \( \lambda_C = \frac{h}{m_ec} \), where \( h \) is Planck's constant, \( m_e \) is the mass of the electron, and \( c \) is the speed of light. The Compton wavelength is indeed very small, on the order of \( 10^{-12} \) meters, which is much smaller than the wavelengths of X-rays typically used in diffraction experiments.

- **Conclusion:** Statement 2 is **true**.

### Final Conclusion
- Statement 1 is false.
- Statement 2 is true.

Thus, the correct option is that Statement 1 is false and Statement 2 is true.