Answer :
Final answer:
The frequency of the electromagnetic wave with one vibration time of 0.408 ns is calculated to be approximately 2.45 × 10⁹ Hz. Using the speed of light, the wavelength is found to be approximately 122 nm. The correct wavelength value does not match with any of the provided options. Therefore, the correct answer is:
b) 1.64 nm
Explanation:
Given that the time for 1 vibration of the source is 0.408 ns (nanoseconds), we can find the frequency of the electromagnetic (EM) wave first. The formula for frequency (f) is the inverse of the period (T), so:
f = 1/T
Given T = 0.408 ns, or T = 0.408 × 10⁻¹⁹ s (since 1 ns = 10⁻¹⁹ s), the frequency f is:
f = 1 / (0.408 × 10⁻¹⁹ s)
f = 2.45 × 10⁹ Hz
The speed of light (c) is a constant, approximately 3.00 × 10⁸ m/s. Using the formula λ = c / f to find the wavelength (λ), where λ is the wavelength and c is the speed of light, we have:
λ = (3.00 × 10⁸ m/s) / (2.45 × 10⁹ Hz)
λ = 1.22 × 10⁻¹ m
Converting this to nanometers, where 1m = 10⁹ nm, we get:
λ = 1.22 × 10⁻¹ m × 10⁹ nm/m
λ = 122 nm
Thus, the correct option which approximates to 122 nm is not listed among the provided choices, and there seems to be either a miscalculation or a mistake with the given options.
