To solve the problem, let's break it down step by step.
1. Understand the given data and constants:
- Speed of light, [tex]\( c = 300,000,000 \text{ meters per second} \)[/tex]
- Wavelength of green laser light, [tex]\( \lambda = 532 \text{ nanometers} \)[/tex]
- Conversion factor, [tex]\( 1 \text{ meter} = 1,000,000,000 \text{ nanometers} \)[/tex]
2. Convert the wavelength from nanometers to meters:
[tex]\[
\lambda_{\text{green}} = \frac{532 \text{ nm}}{1,000,000,000} = 532 \times 10^{-9} \text{ meters} = 5.32 \times 10^{-7} \text{ meters}
\][/tex]
3. Calculate the frequency of the green laser light using the formula:
[tex]\[
v = \frac{c}{\lambda}
\][/tex]
Substituting the values,
[tex]\[
v_{\text{green}} = \frac{300,000,000 \text{ m/s}}{5.32 \times 10^{-7} \text{ m}} \approx 563,909,774,436,090.1 \text{ Hz}
\][/tex]
4. Determine the frequency of the material before doubling:
Given that the material emits light which is then doubled in frequency,
[tex]\[
v_{\text{before doubling}} = \frac{v_{\text{green}}}{2} = \frac{563,909,774,436,090.1 \text{ Hz}}{2} \approx 281,954,887,218,045.06 \text{ Hz}
\][/tex]
5. Compare to the given options:
[tex]\[
\approx 2.8 \times 10^{14} \text{ Hz}
\][/tex]
Therefore, the correct answer is:
B. [tex]\(2.8 \times 10^{14} \text{ Hz}\)[/tex]
