The question asks to arrange various types of electromagnetic (EM) waves in the ascending order of their wavelength. To do this, we need to understand the electromagnetic spectrum, which is the range of all types of EM radiation. Radiation is energy that travels and spreads out as it goes, and it includes visible light, radio waves, X-rays, and many other forms.

Wavelength of Electromagnetic Waves

Electromagnetic waves are characterized by their wavelength and frequency. Wavelength is the distance between successive crests of a wave, while frequency is the number of waves that pass a fixed point in unit time. These two properties are inversely related: a longer wavelength means a lower frequency, and a shorter wavelength means a higher frequency. The electromagnetic spectrum is typically ordered by wavelength (or frequency).

The standard order of electromagnetic waves from the shortest wavelength (highest frequency) to the longest wavelength (lowest frequency) is:

• Gamma rays
• X-rays
• Ultraviolet (UV) rays
• Visible light
• Infrared (IR) rays
• Microwaves
• Radio waves (which include FM and AM radio waves)

Within radio waves, FM (Frequency Modulation) radio waves generally have shorter wavelengths than AM (Amplitude Modulation) radio waves. This is because FM typically operates at higher frequencies than AM.

Arranging Wavelengths in Ascending Order

Now, let's arrange the given electromagnetic waves from the question in ascending order of their wavelength, using the general order of the electromagnetic spectrum:

1. Gamma rays (v): These have the shortest wavelengths among all electromagnetic waves.
2. X-rays (vi): X-rays come after gamma rays and have very short wavelengths.
3. Visible rays (iii): These are the light waves we can see, with wavelengths longer than X-rays but shorter than infrared rays.
4. Infrared rays (ii): Infrared waves have longer wavelengths than visible light but are shorter than microwaves.
5. Microwaves (i): Microwaves have longer wavelengths than infrared rays but are shorter than most radio waves.
6. FM radio waves (vii): These are a type of radio wave. FM waves generally have shorter wavelengths compared to AM radio waves.
7. AM radio waves (iv): AM radio waves have the longest wavelengths among the options provided, extending even further than FM radio waves.

Therefore, the correct ascending order of wavelength for the given electromagnetic waves is:

(v) Gamma rays < (vi) X-rays < (iii) Visible rays < (ii) Infrared rays < (i) Microwaves < (vii) FM radio waves < (iv) AM radio waves

This sequence corresponds to the order: (v), (vi), (iii), (ii), (i), (vii) and (iv).