Question

What is the frequency of yellow light having wavelength 580 nm?

• A. $193 \times 10^{-9}\ \text{Hz}$
• B. $517 \times 10^{-14}\ \text{Hz}$
• C. $5.17 \times 10^{14}\ \text{Hz}$
• D. $580 \times 10^{-9}\ \text{Hz}$

Hint:

Always double-check your exponent signs! Visible light waves always feature extremely high frequencies on the order of $10^{14}\ \text{Hz}$. Remembering this general magnitude threshold lets you instantly eliminate options (A), (B), and (D) without calculating!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem provides the wavelength ($\lambda$) of a yellow light wave as $580\ \text{nm}$. We need to compute its corresponding electromagnetic frequency ($\nu$).

Step 2: Key Formula or Approach:
The frequency and wavelength of any electromagnetic radiation traveling through a vacuum or air are inversely related to the speed of light ($c$) by the equation:
$$c = \lambda \nu \implies \nu = \frac{c}{\lambda}$$ Where the speed of light constant $c \approx 3 \times 10^8\ \text{m/s}$.

Step 3: Detailed Explanation:
Let's convert the given wavelength metric into standard SI units (meters):
$$\lambda = 580\ \text{nm} = 580 \times 10^{-9}\ \text{m} = 5.8 \times 10^{-7}\ \text{m}$$ Now, substitute the values of $c$ and $\lambda$ into our rearranged frequency formula:
$$\nu = \frac{3 \times 10^8\ \text{m/s}}{5.8 \times 10^{-7}\ \text{m}}$$ $$\nu = \frac{3}{5.8} \times 10^{15}\ \text{Hz}$$ Let's compute the fraction fractionally:
$$\frac{3}{5.8} \approx 0.51724$$ $$\nu = 0.51724 \times 10^{15}\ \text{Hz} = 5.1724 \times 10^{14}\ \text{Hz}$$ Rounding this to two decimal places yields $5.17 \times 10^{14}\ \text{Hz}$, which matches option (C).

Step 4: Final Answer:
The frequency of the yellow light wave is $5.17 \times 10^{14}\ \text{Hz}$, which corresponds to option (C).