What is the wavelength of a yellow light with a frequency of [tex]5.2 \times 10^{14} \text{ Hz}[/tex]?

Given:
[tex]\[ c = 3.0 \times 10^8 \text{ m/s} \][/tex]

Be sure to enter both the coefficient and the exponent.



Answer :

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].