In Davisson-Germer experiment, the correct relation between angle of diffraction `phi` and glancing angle `theta` is-

Options

A. `theta = 90^(@) - (phi)/2`
B. `phi = (theta)/(2) - 90^@`
C. `theta = 90^@ - theta`
D. `theta = 90^(@) - theta`

Answer

To solve the problem regarding the relationship between the angle of diffraction \( \phi \) and the glancing angle \( \theta \) in the Davisson-Germer experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Experiment**: The Davisson-Germer experiment demonstrated the wave nature of electrons through diffraction. In this experiment, electrons are scattered off a crystalline surface, and the angles at which they are scattered are measured.

2. **Define the Angles**:
- Let \( \phi \) be the angle of diffraction, which is the angle at which the electrons are detected after scattering.
- Let \( \theta \) be the glancing angle, which is the angle between the incident beam of electrons and the surface of the crystal.

3. **Establish the Relationship**:
- In diffraction experiments, there is a geometric relationship between the angle of incidence, angle of diffraction, and the glancing angle.
- For the Davisson-Germer experiment, the relationship can be derived from the geometry of the setup.

4. **Derive the Formula**:
- The relationship is given by:
\[ \theta = 90^\circ - \frac{\phi}{2} \]
- This means that the glancing angle \( \theta \) is related to the angle of diffraction \( \phi \) in such a way that as \( \phi \) changes, \( \theta \) adjusts accordingly.

5. **Conclusion**:
- Therefore, the correct relation between the angle of diffraction \( \phi \) and the glancing angle \( \theta \) is:
\[ \theta = 90^\circ - \frac{\phi}{2} \]
- The answer is option (a).