To find the wavelength of a yellow light with a frequency of [tex]\(5.2 \times 10^{14} \text{ Hz}\)[/tex], we use the relationship between the speed of light, frequency, and wavelength. The formula is:
[tex]\[ \lambda = \frac{c}{f} \][/tex]
where:
- [tex]\(\lambda\)[/tex] is the wavelength,
- [tex]\(c\)[/tex] is the speed of light ([tex]\(3.0 \times 10^8 \text{ m/s}\)[/tex]),
- [tex]\(f\)[/tex] is the frequency ([tex]\(5.2 \times 10^{14} \text{ Hz}\)[/tex]).
Substitute the given values into the formula:
[tex]\[ \lambda = \frac{3.0 \times 10^8}{5.2 \times 10^{14}} \][/tex]
To simplify this calculation, first calculate the coefficient:
[tex]\[ \frac{3.0}{5.2} \approx 0.576923076923077 \][/tex]
Next, subtract the exponents in the powers of 10:
[tex]\[ 10^8 - 10^{14} = 10^{8 - 14} = 10^{-6} \][/tex]
Therefore, the wavelength can be expressed as:
[tex]\[ \lambda \approx 0.576923076923077 \times 10^{-6} \text{ meters} \][/tex]
So, the wavelength of the yellow light is approximately:
[tex]\[ 0.576923076923077 \times 10^{-6} \text{ meters} \][/tex]
In scientific notation, this is:
[tex]\[ \lambda \approx 0.576 \times 10^{-6} \text{ meters} \][/tex]
Thus, the coefficient is approximately [tex]\(0.576923076923077\)[/tex] and the exponent is [tex]\(-6\)[/tex].
