To determine if Chayse's results for the UV ray's frequency and wavelength are reasonable, we can calculate the speed of the UV ray using the provided values and then compare it to the known speed of light.
### Step-by-Step Solution
1. Determine the given values:
- Frequency, [tex]\( f = 1.53 \times 10^{16} \)[/tex] Hz
- Wavelength, [tex]\( \lambda = 1.96 \times 10^{-8} \)[/tex] m
2. Recall the relationship between speed, frequency, and wavelength:
[tex]\[
\text{Speed} = \text{Frequency} \times \text{Wavelength}
\][/tex]
Using this relationship:
[tex]\[
\text{Speed} = f \times \lambda
\][/tex]
3. Plug in the given values into the formula and calculate:
[tex]\[
\text{Speed} = (1.53 \times 10^{16} \, \text{Hz}) \times (1.96 \times 10^{-8} \, \text{m})
\][/tex]
[tex]\[
\text{Speed} = 2.9988 \times 10^8 \, \text{m/s}
\][/tex]
4. Compare the calculated speed to the known speed of light:
- The known speed of light in a vacuum is approximately [tex]\( 3 \times 10^8 \)[/tex] m/s.
5. Evaluate reasonableness:
- The calculated speed is [tex]\( 2.9988 \times 10^8 \)[/tex] m/s.
- Although not exactly [tex]\( 3 \times 10^8 \)[/tex] m/s, it is extremely close.
6. Assessment:
- The difference between the calculated speed and the speed of light is marginally slight. However, it is significant enough to not be considered precisely the same. Given the precision needed in scientific measurements and the relative discrepancy, the result [tex]\( (2.9988 \times 10^8 \, \text{m/s}) \)[/tex] can be considered reasonably close, but not entirely matching.
### Conclusion
Based on the calculations:
- The speed of the UV ray calculated from the given frequency and wavelength is [tex]\( 2.9988 \times 10^8 \)[/tex] m/s.
- This is very close to the speed of light ([tex]\( 3 \times 10^8 \)[/tex] m/s), but not exact.
Therefore, while the results are quite close, they are not exactly reasonable due to the small but notable difference from the known speed of light.
