Question

The wavelength of a spectral line of caesium is $460\text{ nm}$. What is the frequency of spectral line?

• A. $4.5 \times 10^8\text{ Hz}$
• B. $6.5 \times 10^{14}\text{ Hz}$
• C. $3 \times 10^9\text{ Hz}$
• D. $5.6 \times 10^{14}\text{ Hz}$

Hint:

Visible light wavelengths (roughly $400\text{ nm}$ to $700\text{ nm}$) always have frequencies in the range of $10^{14}\text{ Hz}$. If you calculate a frequency for visible light and the exponent isn't $14$, you've made a unit conversion error!

Answer 1

The Correct Option is B

Step 1: Use the wave relation.
Speed of light $c = \lambda \nu$, so $\nu = \dfrac{c}{\lambda}$.

Step 2: Fix the units.
$\lambda = 460\ \text{nm} = 4.6 \times 10^{-7}\ \text{m}$ and $c = 3 \times 10^8\ \text{m/s}$.

Step 3: Divide.
$$\nu = \frac{3 \times 10^8}{4.6 \times 10^{-7}} \approx 6.5 \times 10^{14}\ \text{Hz}$$
\[ \boxed{6.5 \times 10^{14}\ \text{Hz}} \]