In x-rays diffraction experiment distance between atomic lattices planes of diffraction grating is 2.8 2.8 x 10 raised to minus 10 m then the maximum wavelength of X rays in metres is

To find the maximum wavelength of X-rays that can be diffracted by a crystal with a given distance between atomic lattice planes, we can use Bragg's Law. This law relates the wavelength of the X-rays to the angle of diffraction and the distance between the planes in the crystal lattice. The formula is expressed as:

Bragg's Law

Bragg's Law is given by the equation:

nλ = 2d sin(θ)

Where:

• n = order of diffraction (an integer, typically 1 for maximum wavelength)
• λ = wavelength of the X-rays
• d = distance between atomic lattice planes
• θ = angle of diffraction

Given Values

In your case, the distance between the atomic lattice planes (d) is:

d = 2.8 x 10^-10 m

For maximum wavelength, we can consider the first order of diffraction (n = 1) and the angle θ to be 90 degrees, which gives us the maximum possible wavelength. At this angle, sin(θ) equals 1.

Calculating Maximum Wavelength

Substituting the values into Bragg's Law:

λ = 2d sin(θ)

Since we are using n = 1 and sin(90°) = 1, the equation simplifies to:

λ = 2d

Now, substituting the value of d:

λ = 2 × (2.8 x 10^-10 m)

λ = 5.6 x 10^-10 m

Final Result

The maximum wavelength of the X-rays that can be diffracted by the crystal with the given lattice spacing is:

λ = 5.6 x 10^-10 m

This wavelength falls within the range of X-rays, which typically span from about 0.01 nm to 10 nm. Thus, your calculation aligns well with the properties of X-ray diffraction and the behavior of waves interacting with crystal lattices.