You are conducting experiments with your x-ray diffractometer.

(a) A specimen of molybdenum is exposed to a beam of monochromatic x-rays of wavelength set by the Kα line of silver. Calculate the value of the smallest Bragg angle, θhkl, at which you can expect to observe reflections from the molybdenum specimen.

To calculate the value of the smallest Bragg angle, θhkl, at which you can expect to observe reflections from the molybdenum specimen, we need to use the Bragg's law equation:

nλ = 2d sin(θ)

Where:
- n is the order of diffraction,
- λ is the wavelength of x-rays,
- d is the spacing between crystal planes, and
- θ is the Bragg angle.

To calculate the smallest Bragg angle, we need to consider the first order diffraction, n = 1. Additionally, we need the wavelength of the x-rays and the spacing between crystal planes.

1. Wavelength of x-rays:
In this case, the wavelength is set by the Kα line of silver. The wavelength of the Kα line of silver is approximately 0.154 nm (nanometers).

2. Spacing between crystal planes:
For molybdenum, we can use the atomic spacing d(110), which is the distance between crystal planes perpendicular to the crystallographic (110) direction. For molybdenum, d(110) is approximately 0.314 nm.

Now, let's plug the values into the equation:

1 * (0.154 nm) = 2 * (0.314 nm) * sin(θ)

Simplifying the equation:

0.154 nm = 0.628 nm * sin(θ)

Divide both sides of the equation by 0.628 nm:

sin(θ) = 0.154 nm / 0.628 nm

sin(θ) ≈ 0.2458

Now, take the inverse sine (sin^(-1)) of both sides:

θ ≈ sin^(-1)(0.2458)

Using a scientific calculator or an online calculator, the approximate value of θ is:

θ ≈ 14.2°

Therefore, the smallest Bragg angle, θhkl, at which you can expect to observe reflections from the molybdenum specimen is approximately 14.2°.