To determine the frequency and wavelength of an electromagnetic (EM) wave given its energy, we can use the relationship between energy (E), frequency (ν), and Planck's constant (h):
E = hν
where h is the Planck's constant, approximately 6.626 × 10^(-34) J·s.
Rearranging the equation, we can solve for the frequency:
ν = E / h
Given the energy E as 6.626 × 10^(-19) J, and using the value for Planck's constant, we can calculate the frequency:
ν = (6.626 × 10^(-19) J) / (6.626 × 10^(-34) J·s)
ν ≈ 1.0 × 10^15 Hz
Now, to find the wavelength (λ) of the EM wave, we can use the speed of light (c) and the frequency:
c = λν
where c is approximately 3 × 10^8 m/s.
Rearranging the equation, we can solve for the wavelength:
λ = c / ν
Substituting the values, we have:
λ = (3 × 10^8 m/s) / (1.0 × 10^15 Hz)
λ ≈ 3 × 10^(-7) m or 300 nm
Therefore, an EM wave with an energy of approximately 6.626 × 10^(-19) J has a frequency of 1.0 × 10^15 Hz and a wavelength of 300 nm.