The range of wavelengths of the infrared waves in an electromagnetic spectrum is $10^{-3}$ m  to $10^{-6}$m. The wavelength of the radiation is

Analyze the question: The question is incomplete as written ("The wavelength of the radiation is..."). It most likely means "the wavelength of infrared radiation compared with other parts of the spectrum," or it asks which statement fits the range given. Let's work from the information we have.

Concept: The electromagnetic spectrum, from longest to shortest wavelength, is:

Radio waves → Microwaves → Infrared → Visible light → Ultraviolet → X-rays → Gamma rays

Infrared waves lie between microwaves and visible light. Visible light has wavelengths of about 4×10⁻⁷ m to 7×10⁻⁷ m, which is shorter than 10⁻⁶ m. So infrared is longer than visible light, and its wavelengths are longer than about 10⁻⁶ m, up to 10⁻³ m.

Checking the options against the given range (10⁻⁶ m to 10⁻³ m):

• A. Longer than 10⁻⁶ m: the infrared range starts at 10⁻⁶ m and goes upward, so every infrared wavelength is longer than (or at least equal to) 10⁻⁶ m. This is consistent.
• B. Shorter than 10⁻⁶ m: this would be visible light, UV and beyond, not infrared.
• C. Shorter than 10³ m: this is technically true, since 10⁻³ m is much less than 10³ m. But it is a very loose statement that does not describe infrared. It would be true of almost every wave in the spectrum except long radio waves.
• D. Longer than 10³ m: this is false, since infrared is at most 10⁻³ m.

Note on the wording: Options A and C are both literally true for the given range, so the question is ambiguous. The most meaningful statement that identifies infrared, as opposed to visible light and shorter waves, is that its wavelength is longer than 10⁻⁶ m.

Answer: A

Tip: Memorize the spectrum order, "Rich Men In Very Ugly X-Gear" (Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma). Moving from left to right, wavelength decreases and frequency increases. Infrared sits just beyond red light, so its wavelength is longer than that of visible light.