To find the wavelength of yellow light, we can use the formula that relates the speed of light (c), frequency (f), and wavelength (λ):
\[ c = f \times \lambda \]
Rearranging this formula to solve for the wavelength gives us:
\[ \lambda = \frac{c}{f} \]
Given:
- Speed of light, \(c = 3.0 \times 10^8 \text{ m/s}\)
- Frequency, \(f = 5.2 \times 10^{14} \text{ Hz}\)
Now, we can substitute the values into the equation:
\[ \lambda = \frac{3.0 \times 10^8 \text{ m/s}}{5.2 \times 10^{14} \text{ Hz}} \]
Calculating this gives us:
\[ \lambda = \frac{3.0}{5.2} \times \frac{10^8}{10^{14}} \text{ m} \]
Calculating the numerical part:
\[ \frac{3.0}{5.2} \approx 0.5769 \]
Now for the powers of ten:
\[ \frac{10^8}{10^{14}} = 10^{-6} \]
Now putting it all together:
\[ \lambda \approx 0.5769 \times 10^{-6} \text{ m} \]
Converting this to scientific notation:
\[ \lambda \approx 5.769 \times 10^{-7} \text{ m} \]
Rounding this to two significant figures gives:
\[ \lambda \approx 5.8 \times 10^{-7} \text{ m} \]
Thus, the wavelength of yellow light is \( \mathbf{5.8 \times 10^{-7} \text{ m}} \).
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