Question

1. Calculate the wavelength of the electromagnetic radiation with frequency 3x1014 Hz. What is the type of radiation (Gamma rays, Visible, IR etc.)?

Answer 1

Answer on Question 66561, Physics, Optics

Question:

Calculate the wavelength of the electromagnetic radiation with frequency $3 \cdot 10^{14} \, \text{Hz}$. What is the type of radiation (Gamma rays, Visible, IR etc.)?

Solution:

For the electromagnetic waves, frequency has an inverse relationship to the wavelength $\lambda$:

$$f = \frac{c}{\lambda},$$

here, $f$ is frequency, $c$ is the speed of light in vacuum and $\lambda$ is the wavelength.

So, from this formula we can find the wavelength $\lambda$:

$$\lambda = \frac{c}{f} = \frac{3.0 \cdot 10^{8} \, \frac{\text{m}}{\text{s}}}{3.0 \cdot 10^{14} \, \text{Hz}} = 1.0 \cdot 10^{-6} \, \text{m} = 1.0 \, \mu\text{m} = 1000 \, \text{nm}.$$

If we look at the electromagnetic spectrum scale, we can see that the radiation with the calculated wavelength $\lambda = 1000 \, \text{nm}$ corresponds to the infrared radiation (from $700 \, \text{nm}$ to $1000000 \, \text{nm}$).

Answer:

$\lambda = 1000 \, \text{nm}$, infrared radiation.

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