What is the wavelength of a
UV light with a frequency
of ?
Give your answer in proper scientific notation.

Enter the coefficient in the green box and the
exponent in the yellow box.

Ask by Harper Guzman. in the United States

Jan 24,2025

Question

What is the wavelength of a
UV light with a frequency
of ?
Give your answer in proper scientific notation.

Enter the coefficient in the green box and the
exponent in the yellow box.

Ask by Harper Guzman. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To find the wavelength ($$ \lambda $$) of UV light given its frequency ($$ f $$), we can use the formula:

$$
\lambda = \frac{c}{f}
$$

where:
- $$ c $$ is the speed of light ($$ 3.0 \times 10^{8} \, \mathrm{m/s} $$)
- $$ f $$ is the frequency ($$ 8.8 \times 10^{17} \, \mathrm{Hz} $$)

Now, let's calculate the wavelength step by step.

1. Substitute the known values into the formula:

$$
\lambda = \frac{3.0 \times 10^{8} \, \mathrm{m/s}}{8.8 \times 10^{17} \, \mathrm{Hz}}
$$

2. Perform the division:

$$
\lambda = \frac{3.0}{8.8} \times \frac{10^{8}}{10^{17}}
$$

3. Calculate $$ \frac{3.0}{8.8} $$:

$$
\frac{3.0}{8.8} \approx 0.340909
$$

4. Calculate $$ \frac{10^{8}}{10^{17}} $$:

$$
\frac{10^{8}}{10^{17}} = 10^{8-17} = 10^{-9}
$$

5. Combine the results:

$$
\lambda \approx 0.340909 \times 10^{-9} \, \mathrm{m}
$$

6. Convert $$ 0.340909 $$ into proper scientific notation:

$$
0.340909 = 3.40909 \times 10^{-1}
$$

7. Therefore, we can express $$ \lambda $$ as:

$$
\lambda \approx 3.40909 \times 10^{-1} \times 10^{-9} = 3.40909 \times 10^{-10} \, \mathrm{m}
$$

Now, rounding $$ 3.40909 $$ to three significant figures gives us $$ 3.41 $$.

Thus, the final answer in scientific notation is:

$$
\lambda \approx 3.41 \times 10^{-10} \, \mathrm{m}
$$

So, the coefficient is $$ 3.41 $$ and the exponent is $$ -10 $$.
The wavelength is $$ 3.41 \times 10^{-10} $$ meters.