Question

what is the frequency, in s⁻¹, of blue light with a wavelength of 465 nm?
6.45 x 10¹⁴ s⁻¹
4.65 x 10¹⁴ s⁻¹
4.65 s⁻¹
465 s⁻¹
1.35 x 10¹⁴ s⁻¹

Explanation:

Step1: Recall the formula relating speed, wavelength, and frequency

The formula is \( c = \lambda
u \), where \( c \) is the speed of light (\( c = 3.00 \times 10^8 \, \text{m/s} \)), \( \lambda \) is the wavelength, and \(
u \) is the frequency. We need to solve for \(
u \), so \(
u=\frac{c}{\lambda} \).

Step2: Convert wavelength to meters

The wavelength is \( 465 \, \text{nm} \). Since \( 1 \, \text{nm} = 10^{-9} \, \text{m} \), we have \( \lambda = 465 \times 10^{-9} \, \text{m}=4.65\times 10^{-7} \, \text{m} \).

Step3: Calculate the frequency

Substitute \( c = 3.00\times 10^{8} \, \text{m/s} \) and \( \lambda = 4.65\times 10^{-7} \, \text{m} \) into the formula \(
u=\frac{c}{\lambda} \).

\(
u=\frac{3.00\times 10^{8} \, \text{m/s}}{4.65\times 10^{-7} \, \text{m}} \)

First, divide the coefficients: \( \frac{3.00}{4.65}\approx0.645 \)

Then, divide the powers of 10: \( \frac{10^{8}}{10^{-7}} = 10^{8 - (-7)}=10^{15} \)

But wait, we made a mistake in the exponent calculation. Wait, \( \lambda = 465 \, \text{nm}=465\times 10^{-9} \, \text{m} = 4.65\times 10^{-7} \, \text{m} \) (since \( 465\times 10^{-9}=4.65\times 10^{2}\times 10^{-9}=4.65\times 10^{-7} \)). Then \( \frac{3.00\times 10^{8}}{4.65\times 10^{-7}}=\frac{3.00}{4.65}\times 10^{8 + 7}=\frac{3.00}{4.65}\times 10^{15}\approx0.645\times 10^{15}=6.45\times 10^{14} \, \text{s}^{-1} \)

Answer:

\( 6.45 \times 10^{14} \, \text{s}^{-1} \) (the first option: \( 6.45 \times 10^{14} \, \text{s}^{-1} \))