Final Answer:
a) \(5.99 \times 10^{14}\) Hz
b) \(1.99 \times 10^{14}\) Hz
c) \(3.00 \times 10^{9}\) Hz
d) \(3.00 \times 10^{16}\) Hz
Step-by-step explanation:
The frequency (\(v\)) of electromagnetic radiation can be calculated using the speed of light (\(c\)) formula: \(v = \frac{c}{\lambda}\), where \(\lambda\) is the wavelength.
a) For \(λ = 500 \, \text{nm}\):
\[ v = \frac{3.00 \times 10^8 \, \text{m/s}}{500 \times 10^{-9} \, \text{m}} \approx 5.99 \times 10^{14} \, \text{Hz} \]
b) For \(λ = 1.5 \, \mu\text{m}\):
\[ v = \frac{3.00 \times 10^8 \, \text{m/s}}{1.5 \times 10^{-6} \, \text{m}} \approx 1.99 \times 10^{14} \, \text{Hz} \]
c) For \(λ = 10 \, \text{cm}\):
\[ v = \frac{3.00 \times 10^8 \, \text{m/s}}{10 \, \text{cm}} = 3.00 \times 10^9 \, \text{Hz} \]
d) For \(λ = 0.01 \, \text{Å}\) (Note: 1 Å = \(1 \times 10^{-10}\) m):
\[ v = \frac{3.00 \times 10^8 \, \text{m/s}}{0.01 \times 10^{-10} \, \text{m}} = 3.00 \times 10^{16} \, \text{Hz} \]
These frequencies represent the number of cycles per second for each corresponding wavelength of electromagnetic radiation.