To find the wavelength of light given its frequency, we can use the formula that relates the speed of light (c), frequency (f), and wavelength (λ):
\[ c = \lambda \cdot f \]
Where:
- \( c \) is the speed of light, approximately \( 3.0 \times 10^8 \) meters per second (m/s),
- \( f \) is the frequency in hertz (Hz),
- \( \lambda \) is the wavelength in meters (m).
We can rearrange this formula to solve for wavelength \( \lambda \):
\[ \lambda = \frac{c}{f} \]
Given:
- \( f = 5.0 \times 10^{14} \) Hz,
- \( c = 3.0 \times 10^8 \) m/s.
Now we can plug in the values:
\[ \lambda = \frac{3.0 \times 10^8 , \text{m/s}}{5.0 \times 10^{14} , \text{Hz}} \]
Calculating this gives:
\[ \lambda = \frac{3.0}{5.0} \times \frac{10^8}{10^{14}} = 0.6 \times 10^{-6} \text{ m} \]
Thus, converting \( 0.6 \times 10^{-6} , \text{m} \) to nanometers (1 m = \( 10^9 \) nm):
\[ \lambda = 0.6 \times 10^{-6} \text{ m} \times 10^9 \text{ nm/m} = 600 \text{ nm} \]
Therefore, the wavelength of the yellow light is approximately 600 nm.