Question

Calculate the frequency if wavelength is 750 nm.

• A. 2 x 10^14 Hz
• B. 4 x 10^14 Hz
• C. 6 x 10^15 Hz
• D. 8 x 10^15 Hz

Hint:

Remember the fundamental relationship $c = \lambda \nu$ for electromagnetic waves. Always convert wavelength to meters before calculations if the speed of light is in m/s.

Answer 1

The Correct Option is A

Step 1: Recall the relationship between speed of light, wavelength, and frequency.\ The speed of light ($c$), wavelength ($\lambda$), and frequency ($\nu$) are related by the equation:\ \[c = \lambda \cdot \nu\]\ Where:\ $c$ is the speed of light in a vacuum, approximately $3 \times 10^{8} \text{ m/s}$.\ $\lambda$ is the wavelength in meters.\ $\nu$ is the frequency in hertz (Hz).\
Step 2: Convert the given wavelength to meters.\ The given wavelength is $750 \text{ nm}$. Since $1 \text{ nm} = 10^{-9} \text{ m}$, we convert:\ \[\lambda = 750 \text{ nm} = 750 \times 10^{-9} \text{ m}\]\ \[\lambda = 7.50 \times 10^{2} \times 10^{-9} \text{ m} = 7.50 \times 10^{-7} \text{ m}\]\
Step 3: Rearrange the formula to solve for frequency.\ From the relationship $c = \lambda \cdot \nu$, we can express frequency as:\ \[\nu = \frac{c}{\lambda}\]\
Step 4: Substitute the values and calculate the frequency.\ \[\nu = \frac{3 \times 10^{8} \text{ m/s{7.50 \times 10^{-7} \text{ m\]\ \[\nu = \frac{3}{7.50} \times 10^{8 - (-7)} \text{ Hz}\]\ \[\nu = 0.4 \times 10^{15} \text{ Hz}\]\ \[\nu = 4 \times 10^{-1} \times 10^{15} \text{ Hz}\]\ \[\nu = 4 \times 10^{14} \text{ Hz}\]\
Step 5: Compare with the given options.\ The calculated frequency is $4 \times 10^{14} \text{ Hz}$, which matches Option B.