Problem — Ranking common wavelengths

Problem

Rank the following radiations by decreasing wavelength:

• (A) remote-control infrared, $\lambda\sim 10^{-6}$ m;
• (B) oven microwaves, $\lambda\sim 0{,}12$ m;
• (C) X-rays, $\lambda\sim 10^{-10}$ m;
• (D) WiFi at $2{,}4$ GHz, $\lambda\sim 0{,}12$ m.

What do B and D have in common?

Solution

Comparing the wavelengths. Let’s list the values: $B=D\approx 0{,}12\ \text{m},\qquad A\approx 10^{-6}\ \text{m},\qquad C\approx 10^{-10}\ \text{m}$

From largest to smallest: $0{,}12>10^{-6}>10^{-10}$. The two microwaves B and D coincide and are the longest; then comes infrared A; last are X-rays, the shortest.

What B and D have in common. WiFi at $2{,}4$ GHz and the microwave oven are in the same band (microwaves). Check with $\lambda=c/f$ for WiFi: $\lambda=\frac{3{,}00\cdot 10^8}{2{,}4\cdot 10^9}\approx 0{,}125\ \text{m}$ practically the same $\lambda$ as the oven: this is why the oven emits precisely in the microwave region, close to WiFi frequencies.

Final ranking: $\ev{B\approx D>A>C}$

Connections

Topics: Electromagnetic waves Concepts: Electromagnetic wave Skills: Ranking reasoning