If λv, λx and λm represent the wavelengths of visible light, X-rays and microwaves respectively, thenλm > λx > λvλm > λv > λxλv > λx > λmλv > λm > λx

To analyze the given inequalities involving the wavelengths of visible light (λv), X-rays (λx), and microwaves (λm), we need to consider the characteristics of these types of electromagnetic radiation.

Understanding Wavelengths

1. Microwaves (λm) have the longest wavelengths compared to visible light and X-rays. They typically range from about 1 millimeter to 30 centimeters.
2. Visible Light (λv) has a medium wavelength, which ranges from approximately 400 nanometers (violet) to around 700 nanometers (red).
3. X-rays (λx) have the shortest wavelengths among these three, generally ranging from 0.01 to 10 nanometers.

Establishing Inequalities

Based on the descriptions above, we can establish the following order of wavelengths from longest to shortest:

• Microwaves (λm) > Visible Light (λv) > X-rays (λx)

Analyzing the Provided Options

Now, let’s analyze the provided inequalities:

1. λm > λx > λv: Incorrect, as λm (microwaves) should be greater than λv (visible light).
2. λm > λv > λx: Correct, as established by our understanding of the electromagnetic spectrum.
3. λv > λx > λm: Incorrect, since λm is greater than both λv and λx.
4. λv > λm > λx: Incorrect for the same reason as above.
5. λv > λx > λm: Incorrect, λm should be the largest.
6. λv > λm > λx: Incorrect.
7. λm > λv > λx: Correct.
8. λm > λx > λv: Incorrect.

Final Conclusion

The only correct statement based on the characteristics of the wavelengths is λm > λv > λx. This matches our ordered understanding of the wavelengths in the electromagnetic spectrum.