Question:easy

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

Show 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!
Updated On: Jun 8, 2026
  • $4.5 \times 10^8\text{ Hz}$
  • $6.5 \times 10^{14}\text{ Hz}$
  • $3 \times 10^9\text{ Hz}$
  • $5.6 \times 10^{14}\text{ Hz}$
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Understand the question.
A spectral line has wavelength $460\,\text{nm}$. We must find its frequency.

Step 2: Recall the wave relation.
For light, speed equals wavelength times frequency, $c = \lambda \nu$. So \[ \nu = \frac{c}{\lambda} \] with $c = 3 \times 10^8\ \text{m s}^{-1}$.

Step 3: Fix the units of wavelength.
Change nanometres into metres: $460\,\text{nm} = 460 \times 10^{-9}\,\text{m} = 4.6 \times 10^{-7}\,\text{m}$.

Step 4: Put the values in.
\[ \nu = \frac{3 \times 10^8}{4.6 \times 10^{-7}} \]
Step 5: Do the arithmetic.
Dividing $3$ by $4.6$ gives about $0.652$, and the powers of ten give $10^{8-(-7)} = 10^{15}$. So \[ \nu = 0.652 \times 10^{15} = 6.52 \times 10^{14}\ \text{Hz} \]
Step 6: Pick the answer.
Rounded, this is $6.5 \times 10^{14}\,\text{Hz}$, option (B).
\[ \boxed{\nu = 6.5 \times 10^{14}\ \text{Hz}} \]
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