An electromagnetic wave has a frequency of $6.0 \times 10^{18} Hz$. What is the wavelength of the wave? Use the equation $\lambda=\frac{v}{f}$ and the speed of light as 3.0 $\times 10^8 m / s$.
A. $5.0 \times 10^{-11} m$
B. $2.0 \times 10^{-26} m$
C. $5.0 \times 10^{26} m$
D. $2.0 \times 10^{10} m
Answer (2)
Substitute the given values of speed of light v = 3.0 × 1 0 8 m / s and frequency f = 6.0 × 1 0 18 Hz into the equation λ = f v .
Calculate the wavelength: λ = 6.0 × 1 0 18 3.0 × 1 0 8 = 0.5 × 1 0 − 10 m .
Convert to scientific notation: λ = 5.0 × 1 0 − 11 m .
The wavelength of the electromagnetic wave is 5.0 × 1 0 − 11 m .
Explanation
Understanding the Problem We are given the frequency of an electromagnetic wave, f = 6.0 × 1 0 18 Hz , and the speed of light, v = 3.0 × 1 0 8 m / s . We need to find the wavelength, λ , using the equation λ = f v .
Substituting the Values Now, we substitute the given values into the equation: λ = 6.0 × 1 0 18 Hz 3.0 × 1 0 8 m / s
Calculating the Wavelength Performing the calculation: λ = 6.0 3.0 × 1 0 18 1 0 8 m = 0.5 × 1 0 8 − 18 m = 0.5 × 1 0 − 10 m = 5.0 × 1 0 − 11 m
Final Answer Therefore, the wavelength of the electromagnetic wave is 5.0 × 1 0 − 11 m .
Examples
Electromagnetic waves are used in various applications such as radio communication, medical imaging, and sterilization. For example, X-rays, which are electromagnetic waves with very short wavelengths (on the order of 1 0 − 8 to 1 0 − 12 meters), are used in medical imaging to visualize bones and internal organs. Knowing the relationship between frequency and wavelength allows scientists and engineers to design and utilize electromagnetic waves effectively in these applications.
The wavelength of the electromagnetic wave with a frequency of 6.0 × 1 0 18 Hz is calculated to be 5.0 × 1 0 − 11 m using the formula λ = f v . The chosen option is A.
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