Question

The wavelength of blue light is 480 nm. What is frequency of this light?

• A. $4.8 \times 10^9$ Hz
• B. $2.25 \times 10^{14}$ Hz
• C. $6.25 \times 10^{14}$ Hz
• D. $5.25 \times 10^9$ Hz

Hint:

When performing calculations with $\nu = c / \lambda$, you can bypass traditional division by simplifying numbers mentally first. Recognizing that $3 / 4.8$ is identical to the fractional value $5 / 8$ allows you to quickly write down $0.625$ without setting up a long division table.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the wavelength ($\lambda = 480\text{ nm}$) of a beam of blue light and need to calculate its corresponding electromagnetic frequency ($\nu$).

Step 2: Key Formula or Approach:
The frequency and wavelength of any electromagnetic radiation traveling through a vacuum are inversely linked by the constant speed of light ($c$): $$c = \lambda \times \nu$$ Rearranging to isolate and solve for the frequency ($\nu$) gives: $$\nu = \frac{c}{\lambda}$$ Where the speed of light $c \approx 3.0 \times 10^8\text{ m s}^{-1}$.

Step 3: Detailed Explanation:
1. Convert the wavelength from nanometers to meters to match standard SI base units: $$\lambda = 480\text{ nm} = 480 \times 10^{-9}\text{ m} = 4.8 \times 10^{-7}\text{ m}$$ 2. Substitute the values into our frequency calculation formula: $$\nu = \frac{3.0 \times 10^8\text{ m s}^{-1}}{4.8 \times 10^{-7}\text{ m}}$$ 3. Separate the numerical division from the exponent handling to minimize arithmetic slipups: $$\nu = \left(\frac{3}{4.8}\right) \times 10^{8 - (-7)}$$ $$\nu = 0.625 \times 10^{15}\text{ Hz}$$ 4. Shifting the decimal into proper standard scientific notation yields: $$\nu = 6.25 \times 10^{14}\text{ Hz}$$

Step 4: Final Answer:
The frequency of the blue light is $6.25 \times 10^{14}\text{ Hz}$, corresponding exactly to option (C).