Question

what is the wavelength (in nanometers) of a photon of light with an energy of 3.82×10⁻¹⁸j? report your answer to the correct number sig figs by filling in the blanks below with the units given last; do not use scientific notation.

question 4
if the laser with a frequency of 2.871×10¹⁵ hz emits 1.55 mj of energy during a pulse, how many photons are emitted? report your answer in scientific notation to the correct number of sig figs by filling in the blanks below. do not include units in your answer.

question 5
in what region of the electromagnetic spectrum would you find a photon with an energy of 5.33×10⁻²³ j?

Explanation:

Step1: Recall energy - wavelength formula

The energy of a photon is given by $E = h
u=\frac{hc}{\lambda}$, where $E$ is energy, $h = 6.626\times10^{-34}\text{ J}\cdot\text{s}$ (Planck's constant), $c= 3.00\times 10^{8}\text{ m/s}$ (speed of light) and $\lambda$ is wavelength. We can re - arrange for $\lambda$: $\lambda=\frac{hc}{E}$.

Step2: Calculate wavelength for first question

Substitute $h = 6.626\times10^{-34}\text{ J}\cdot\text{s}$, $c = 3.00\times10^{8}\text{ m/s}$ and $E=3.82\times 10^{-18}\text{ J}$ into the formula.
$\lambda=\frac{6.626\times 10^{-34}\text{ J}\cdot\text{s}\times3.00\times 10^{8}\text{ m/s}}{3.82\times 10^{-18}\text{ J}}$.
$\lambda=\frac{19.878\times10^{-26}}{3.82\times 10^{-18}}\text{ m}=5.20\times 10^{-8}\text{ m}$.
Convert to nanometers: $1\text{ m}=10^{9}\text{ nm}$, so $\lambda = 52.0\text{ nm}$.

Step3: Recall energy - photon number formula

The energy of a single photon is $E_{photon}=h
u$, where $
u$ is frequency. Given $
u = 2.871\times10^{15}\text{ Hz}$, $E_{photon}=6.626\times 10^{-34}\text{ J}\cdot\text{s}\times2.871\times 10^{15}\text{ Hz}=1.902\times10^{-18}\text{ J}$.
The total energy of the pulse is $E_{total}=1.55\text{ mJ}=1.55\times 10^{-3}\text{ J}$.
The number of photons $n=\frac{E_{total}}{E_{photon}}$.

Step4: Calculate number of photons for second question

$n=\frac{1.55\times 10^{-3}\text{ J}}{1.902\times 10^{-18}\text{ J}} = 8.15\times10^{14}$ photons.

Step5: Determine electromagnetic region for third question

First, find the frequency using $E = h
u$, so $
u=\frac{E}{h}$. Substitute $E = 5.33\times10^{-23}\text{ J}$ and $h = 6.626\times10^{-34}\text{ J}\cdot\text{s}$.
$
u=\frac{5.33\times 10^{-23}\text{ J}}{6.626\times 10^{-34}\text{ J}\cdot\text{s}}=8.04\times10^{10}\text{ Hz}$.
This frequency corresponds to the microwave region of the electromagnetic spectrum.

Answer:

Question 1: 52.0
Question 2: 8.15, 14
Question 3: Microwave