Diffraction

Step 1: Use the diffraction grating equation.
The diffraction condition for a grating is given by Bragg’s law: where is the diffraction order, is the wavelength of the light, is the grating spacing, and is the diffraction angle.
Step 2: Calculate the grating spacing.
The number of lines per centimeter is 4000, so the grating spacing is:
Step 3: Apply the diffraction equation.
For the third-order maximum ( ) and wavelength : Solving for :
Step 4: Conclusion.
Thus, the diffraction angle corresponding to the third-order maximum is 21.04°.

Step 1: Understanding the X-ray diffraction condition.
For X-ray diffraction, the Bragg’s law is used to determine the angles at which diffraction peaks appear: where is the diffraction order, is the wavelength of the X-rays, is the spacing between the planes, and is the diffraction angle. The first order diffraction peak corresponds to . For a simple cubic structure, the spacing for the planes is given by: where is the lattice parameter and are the Miller indices of the planes.

Step 2: Analyzing the options.
- (A) (100) planes: Correct. The planes have the smallest spacing and will give the first order diffraction peak.
- (B) (112) planes: Incorrect. The spacing for the planes is larger, so they will not correspond to the first order diffraction peak.
- (C) (210) planes: Incorrect. The spacing for the planes is larger than that for the planes.
- (D) (220) planes: Incorrect. The spacing for the planes is also larger than that for the planes.

Step 3: Conclusion.
The correct answer is (A) because the first order diffraction peak appears for the planes, as they have the smallest spacing.

Step 1: Understanding the diffraction pattern.
In the Fraunhofer diffraction pattern for a single slit, intensity minima occur at angles given by the equation: where is the slit width, is the diffraction angle, is the order of the minima, and is the wavelength of the light. The condition for intensity minima is when is an integer (excluding for the central maximum).

Step 2: Calculating the maximum number of minima.
To calculate the maximum number of minima, we use the formula for the angle of the minima and solve for the highest value of where the sine term remains less than or equal to 1: Given and , we find as the maximum number of minima.

Step 3: Conclusion.
The correct answer is (B) 7 because there are 7 intensity minima observable in this diffraction pattern.