$$f = c / \lambda$$
Where:
- \(f\) is the frequency in Hertz (Hz)
- \(c\) is the speed of light (299,792,458 meters per second or 3.00 x 10^8 m/s)
- \(\lambda\) is the wavelength in meters (m)
First, we need to convert the wavelength from Ångströms (\(\text{Å}\)) to meters (\(\text{m}\)):
$$4000\text{Å} = 4000 \times 10^{-10}\text{m}$$
$$= 4.00 \times 10^{-7}\text{m}$$
Now, we can substitute the values of \(c\) and \(\lambda\) into the formula:
$$f = \dfrac{3.00 \times 10^8 \text{m/s}}{4.00 \times 10^{-7}\text{m}}$$
$$f = 7.50 \times 10^{14} \text{Hz}$$
To convert the frequency from Hertz (Hz) to Megahertz (MHz), we divide by 1,000,000:
$$f = \dfrac{7.50 \times 10^{14}\text{Hz}}{1,000,000}$$
$$f = 7.50 \times 10^{8}\text{MHz}$$
Therefore, the frequency of the beam of blue light with a wavelength of 4000 Ångströms is 750 MHz.
