Questions: X-rays have a wavelength small enough to image individual atoms, but are challenging to detect because of their typical frequency. Suppose an X-ray camera uses X-rays with a wavelength of 9.24 nm. Calculate the frequency of the X-rays. Be sure your answer has the correct number of significant digits. PHz

Solution Steps

The frequency (\(f\)) of a wave is related to its wavelength (\(\lambda\)) and the speed of light (\(c\)) by the equation:

\[ f = \frac{c}{\lambda} \]

where:

• \(c\) is the speed of light, approximately \(3.00 \times 10^8 \, \text{m/s}\),
• \(\lambda\) is the wavelength of the X-rays.

The given wavelength is 9.24 nm. We need to convert this to meters for consistency with the speed of light's units:

\[ 9.24 \, \text{nm} = 9.24 \times 10^{-9} \, \text{m} \]

Substitute the values into the frequency equation:

\[ f = \frac{3.00 \times 10^8 \, \text{m/s}}{9.24 \times 10^{-9} \, \text{m}} \]

Calculate the frequency:

\[ f = 3.247 \times 10^{16} \, \text{Hz} \]

1 PHz (petahertz) is \(10^{15}\) Hz. Convert the frequency to PHz:

\[ f = \frac{3.247 \times 10^{16} \, \text{Hz}}{10^{15} \, \text{Hz/PHz}} = 32.47 \, \text{PHz} \]

Final Answer