Let's analyze the situation step-by-step to determine if Chayse's results are reasonable.
### Step 1: Understand the Given Values
Chayse has determined the following characteristics of a UV ray:
- Frequency (\( f \)): \( 1.53 \times 10^{16} \) Hz
- Wavelength (\( \lambda \)): \( 1.96 \times 10^{-8} \) m
### Step 2: Understand the Relationship between Frequency, Wavelength, and the Speed of Light
The speed of light (\( c \)) in a vacuum is a constant value, given by \( c = 3 \times 10^8 \) meters per second (m/s).
The relationship between the speed of light, frequency, and wavelength is given by the equation:
[tex]\[ c = f \times \lambda \][/tex]
### Step 3: Calculate the Product of Frequency and Wavelength
We need to calculate the product of the given frequency and wavelength to see if it approximates the speed of light:
[tex]\[ \text{Product} = (1.53 \times 10^{16} \, \text{Hz}) \times (1.96 \times 10^{-8} \, \text{m}) \][/tex]
Simplifying the numbers inside the parentheses:
- For \( 1.53 \times 1.96 \):
[tex]\[ 1.53 \times 1.96 = 2.9988 \][/tex]
- For the powers of 10, we combine the exponents:
[tex]\[ 10^{16} \times 10^{-8} = 10^{(16-8)} = 10^8 \][/tex]
So the product is:
[tex]\[ \text{Product} = 2.9988 \times 10^8 \, \text{m/s} \][/tex]
### Step 4: Compare the Calculated Product with the Speed of Light
The speed of light is approximately \( 3 \times 10^8 \) m/s. We compare our calculated product to this value:
- Calculated product: \( 2.9988 \times 10^8 \) m/s
- Speed of light: \( 3 \times 10^8 \) m/s
### Step 5: Determine Reasonableness
To determine if Chayse's results are reasonable, we check if the calculated product is close to the speed of light. The calculated product \( 2.9988 \times 10^8 \) m/s is very close to \( 3 \times 10^8 \) m/s. Although there is a tiny difference, it is generally acceptable within measurement tolerances for practical purposes.
Given this comparison, we can conclude that while not exactly equal, the results obtained are very close and, therefore, reasonable.
### Conclusion
Yes, Chayse's results are reasonable because the calculated value of [tex]\( 2.9988 \times 10^8 \)[/tex] m/s is very close to the speed of light value of [tex]\( 3 \times 10^8 \)[/tex] m/s. The small discrepancy can be attributed to rounding or measurement tolerances.
