An electromagnetic wave travelling in a vacuum has a frequency of 3...

The relationship between the speed of light ($c$), frequency ($\nu$), and wavelength ($\lambda$) is given by:
$c = \nu \lambda$

Given:
Frequency, $\nu = 3 \times 10^{13}\text{ Hz}$
Speed of light in vacuum, $c = 3 \times 10^8\text{ m/s}$

Rearranging the formula to solve for wavelength:
$\lambda = \dfrac{c}{\nu}$
$\lambda = \dfrac{3 \times 10^8}{3 \times 10^{13}}$
$\lambda = 10^{-5}\text{ m}$

According to the electromagnetic spectrum, the wavelength range from $10^{-3}\text{ m}$ to $7 \times 10^{-7}\text{ m}$ corresponds to Infrared rays. Therefore, a wavelength of $10^{-5}\text{ m}$ falls in the infrared region.

Multiplying the values instead of dividing leads to the incorrect $9 \times 10^{21}\text{ m}$, and confusing the spectrum ranges leads to incorrectly identifying it as ultraviolet or microwaves.

Answer: $10^{-5}\text{ m}$, Infrared rays