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Chapter 7: Problem 15

Calculate the frequency of light that has a wavelength of \(75.0 \mathrm{~nm}\). What type of radiation is this?

Short Answer

Expert verified
The frequency of the light is \(4.00 \times 10^{15}\) Hz, and it falls in the category of ultraviolet radiation.

Step by step solution

01

Understand and setup the formula.

The formula that relates the speed of light (\(c\)), the wavelength (\(\lambda\)), and the frequency (\(\nu\)) is \(c = \lambda \nu\). Also, understand that the speed of light (\(c\)) is approximately \(3.00 \times 10^8\) meters per second (m/s) and that we'll need to convert the wavelength from nanometers (nm) to meters (m) by multiplying by \(1.00 \times 10^{-9}\). Set up the conversion and the formula first.
02

Convert the wavelength.

Convert the wavelength from nanometers to meters. \(75.0 \mathrm{~nm}\) = \(75.0 \times 1.00 \times 10^{-9}\) meters = \(7.50 \times 10^{-8}\) meters.
03

Calculate the frequency.

Substitute the speed of light (\(c\)) and the wavelength (\(\lambda\)) into the formula \(c = \lambda \nu\). Rearrange the formula to solve for the frequency (\(\nu\)): \(\nu = \frac{c}{\lambda}\) = \(\frac{3.00 \times 10^8 \mathrm{~m/s}}{7.50 \times 10^{-8}\mathrm{~m}}\) = \(4.00 \times 10^{15}\) Hz (Hertz).
04

Identify the type of radiation.

Compare the obtained frequency with the range of frequencies for different types of electromagnetic radiation, and find out where it fits. In this case, a frequency of \(4.00 \times 10^{15}\) Hz falls in the range for ultraviolet radiation.

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Most popular questions from this chapter

In the Bohr model, which of the following electron transitions in a hydrogen atom results in the emission of the highest-energy photon? $$ \begin{aligned} &n=6 \text { to } n=3 \\ &n=5 \text { to } n=3 \end{aligned} $$

What type of radiation has wavelengths just slightly shorter than violet light?

Which type of electromagnetic radiation is composed of the highest-energy photons? Has the longest wavelength? Has the highest frequency?

The wavelength of the blue light emitted from a hydrogen atom is \(410.1 \mathrm{~nm}\). This light is a result of electron transitions from the \(n=5\) to the \(n=2\) energy levels. How much higher in energy is the \(n=5\) energy level than the \(n=2\) energy level?

In the Bohr model, how many photons are emitted when an electron moves directly from the \(n=5\) to the \(n=2\) orbit?
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