Answer:Here are the solutions to the problems:1. Equation to solve for wavelength: λ = c / fFinal answer: λ = c / f2. Wavelength: λ = c / f = (3 x 10^8 m/s) / (1.5 x 10^10 Hz) ≈ 0.02 m or 2 cmType of EM wave: MicrowaveFinal answer: 2 cm, Microwave3. Frequency: f = c / λ = (3 x 10^8 m/s) / (2 x 10^2 m) = 1.5 x 10^6 HzType of EM wave: Radio waveFinal answer: 1.5 x 10^6 Hz, Radio wave4. Solution: f = c / λFinal answer: f = c / λ5. Equation: v = λfFinal answer: v = λf6. Energy: E = hf = (6.63 x 10^-34 J/s) x (5 x 10^15 Hz) ≈ 3.3 x 10^-19 JType of EM wave: UltravioletFinal answer: 3.3 x 10^-19 J, Ultraviolet7. Frequency: f = E / h = (2 x 10^-21 J) / (6.63 x 10^-34 J/s) ≈ 3.02 x 10^12 HzType of EM wave: InfraredFinal answer: 3.02 x 10^12 Hz, Infrared8. Relationship:Energy and Frequency: Directly Proportional (E = hf)Wavelength and Frequency: Inversely Proportional (λ = c / f)Final answer: D, FMatching answers to choices:1. Y (λ = c / f)2. M (2 x 10^2 m, Microwave)3. N (6 x 10^4 Hz, Light)4. Y (f = c / λ)5. A (v = λf)6. U (3.3 x 10^-19 J, Ultraviolet)7. S (3.02 x 10^12 Hz, Infrared)8. D, F (Direct, Inverse)Please note that some answers assume the speed of light (c) as 3 x 10^8 m/s and Planck's constant (h) as 6.63 x 10^-34 J/s.