a cup of hot coffee emits a range of infrared frequencies, but the greatest amount of radiation occurs…

Explanation:

Step1: Recall wave - speed formula

The wave - speed formula is $v = \lambda f$, where $v$ is the speed of light in vacuum ($v = 3\times10^{8}\ m/s$), $\lambda$ is the wavelength, and $f$ is the frequency. We need to solve for $\lambda$.

Step2: Rearrange the formula

Rearranging the formula $v=\lambda f$ for $\lambda$ gives $\lambda=\frac{v}{f}$.

Step3: Substitute the values

We know that $v = 3\times 10^{8}\ m/s$ and $f = 3.55\times10^{13}\ Hz$. Substituting these values into the formula $\lambda=\frac{v}{f}$, we get $\lambda=\frac{3\times 10^{8}}{3.55\times10^{13}}$.

Step4: Perform the calculation

Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\lambda=\frac{3}{3.55}\times10^{8 - 13}$. $\frac{3}{3.55}\approx0.845$ and $10^{8 - 13}=10^{- 5}$. So $\lambda\approx0.845\times10^{-5}\ m$. In scientific notation rounded to two decimal places, $\lambda = 8.45\times10^{-6}\ m$.

Answer:

$8.45\times10^{-6}\ m$