Understanding the Relationship
The relationship between wavelength (λ), frequency (ν), and the speed of light (c) is given by:
c = νλ
* c: Speed of light in a vacuum (approximately 3 x 10⁸ m/s)
* ν: Frequency (in Hertz, Hz)
* λ: Wavelength (in meters, m)
Calculation
1. Rearrange the equation to solve for wavelength (λ):
λ = c / ν
2. Plug in the given values:
λ = (3 x 10⁸ m/s) / (1.5 x 10¹⁸ Hz)
3. Calculate the wavelength:
λ = 2 x 10⁻¹⁰ m
Conclusion
The calculated wavelength of the X-ray with a frequency of 1.5 x 10¹⁸ Hz is 2 x 10⁻¹⁰ meters, which is not 0.20 meters.
The given value of 0.20 meters is incorrect. X-rays have very short wavelengths, typically in the range of nanometers (10⁻⁹ m) or even picometers (10⁻¹² m).
