13. what is the energy of a photon of light with a frequency of 7.66 x 10¹⁴hz\n14. what is the frequency of…

Explanation:

Step1: Recall Planck - Einstein relation

The energy of a photon is given by the formula $E = h\nu$, where $E$ is the energy of the photon, $h$ is Planck's constant ($h=6.63\times 10^{- 34}\text{ J}\cdot\text{s}$), and $\nu$ is the frequency of the photon.

Step2: Solve for question 13

Given $\nu = 7.66\times 10^{14}\text{ Hz}$, we substitute into the formula $E = h\nu$. $E=(6.63\times 10^{-34}\text{ J}\cdot\text{s})\times(7.66\times 10^{14}\text{ Hz})$ Using the rule of exponents $a^m\times a^n=a^{m + n}$, we have $E=(6.63\times7.66)\times10^{-34 + 14}\text{ J}$ $E = 50.7858\times10^{-20}\text{ J}\approx5.08\times 10^{-19}\text{ J}$

Step3: Solve for question 14

We know $E = h\nu$, and we want to find $\nu$. Rearranging the formula gives $\nu=\frac{E}{h}$. Given $E = 8.35\times 10^{-18}\text{ J}$ and $h = 6.63\times 10^{-34}\text{ J}\cdot\text{s}$, then $\nu=\frac{8.35\times 10^{-18}\text{ J}}{6.63\times 10^{-34}\text{ J}\cdot\text{s}}$ Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we get $\nu=\frac{8.35}{6.63}\times10^{-18+34}\text{ Hz}$ $\nu\approx1.26\times 10^{16}\text{ Hz}$

Answer:

13. $5.08\times 10^{-19}\text{ J}$
14. $1.26\times 10^{16}\text{ Hz}$