Solid State And Instrumental Analysis Mock Tests

X-ray diffraction from a crystal with interplanar spacing d = 2.82 Å gives a first-order reflection at a glancing angle of 30°. What is the wavelength of the X-rays used? (Use Bragg's law)

The Cramer's rule is applied to solve simultaneous linear equations in various areas of chemistry. In the context of solving for the composition of a binary mixture using absorbance measurements at two wavelengths, the system of equations is: A₁ = ε₁ₐcₐl + ε₁ᵦcᵦl and A₂ = ε₂ₐcₐl + ε₂ᵦcᵦl. Using Cramer's rule, the concentration cₐ is given by (where Δ = ε₁ₐε₂ᵦ - ε₁ᵦε₂ₐ):

Titanium dioxide (TiO₂) crystallizes in the rutile structure, which can be described as a body-centred tetragonal lattice. In this structure, each Ti⁴⁺ ion is surrounded by 6 O²⁻ ions, and each O²⁻ ion is bonded to 3 Ti⁴⁺ ions. What are the coordination numbers of Ti and O in the rutile structure, and how many formula units of TiO₂ are present per unit cell? (The unit cell contains Ti atoms at the corners and body centre, and O atoms at specific positions within the cell.)

The Bragg angle θ for the first-order reflection (n = 1) from the (110) planes of a cubic crystal with lattice parameter a = 4.00 Å, using X-rays of wavelength λ = 1.54 Å, is approximately:

The IR spectrum of a molecule shows a strong absorption band at 1715 cm⁻¹ and a characteristic C-H stretch at 2720 cm⁻¹. The molecule is most likely:

In the mass spectrum of 2-pentanone (CH₃COCH₂CH₂CH₃), the McLafferty rearrangement produces a characteristic fragment ion. What is the m/z value of the McLafferty rearrangement peak, and what neutral molecule is lost? (The McLafferty rearrangement requires a carbonyl compound with a gamma hydrogen atom relative to the carbonyl group. It involves a six-membered cyclic transition state with transfer of the gamma hydrogen to the carbonyl oxygen, followed by cleavage of the alpha-beta bond.)

The Bragg angle θ for the first-order reflection (n = 1) from the (111) planes of a cubic crystal with lattice parameter a = 4.08 Å, using X-rays of wavelength λ = 1.54 Å, is closest to:

The FTIR spectrum of acetone (CH₃COCH₃) shows a strong absorption at approximately 1715 cm⁻¹. This band corresponds to: