IDNLearn.com: Where your questions are met with thoughtful and precise answers. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.
Sagot :
The possible wavelengths that appear In the emission spectrum of the system are [tex]$210 \mathrm{~nm}, 250 \mathrm{~nm}, 410 \mathrm{~nm}, 620 \mathrm{~nm}, 1200 \mathrm{~nm}$[/tex].
Given:
The quantum energy levels allowed In the system are:
[tex]$\begin{aligned}& E_1=1.0 \mathrm{eV} \\& E_2=2.0 \mathrm{eV} \\& E_3=4.0 \mathrm{eV} \\& E_4=7.0 \mathrm{eV}\end{aligned}$[/tex]
What is wavelength of the emission?
As the transition of electron takes from one energy level to another, there is an emission of particular wavelength from the transition. The relation between the wavelength of the emission and the energy of the energy level Is expressed as:
[tex]$E_f-E_i=\frac{h c}{\lambda}$[/tex]
Here, [tex]$E_f$[/tex] is the final energy level, [tex]$E_i$[/tex] is the Initlal energy level and [tex]$\lambda$[/tex] is the wavelength of emlsslon.
(1). Transition of electron from [tex]$E_1$[/tex] to [tex]$E_2$[/tex] energy level:
[tex]$\begin{aligned}E_2-E_1 & =\frac{h c}{\lambda} \\\lambda & =\frac{\left(6.63 \times 10^{-34}\right) \times\left(3 \times 10^8\right)}{(2-1)\left(1.6 \times 10^{-19}\right)} \mathrm{m} \\& =1.244 \times 10^{-6} \mathrm{~m} \\& \approx 1200 \mathrm{~nm}\end{aligned}$[/tex]
(2). Transition of electron from [tex]$E_1$[/tex] to [tex]$E_3$[/tex] energy level:
[tex]$\begin{aligned}E_3-E_1 & =\frac{h c}{\lambda} \\\lambda & =\frac{\left(6.63 \times 10^{-34}\right) \times\left(3 \times 10^8\right)}{(4-1)\left(1.6 \times 10^{-19}\right)} \mathrm{m} \\& =0.414 \times 10^{-6} \mathrm{~m} \\& \approx 410 \mathrm{~nm}\end{aligned}$[/tex]
(3). Transition of electron from [tex]$E_1$[/tex] to [tex]$E_4$[/tex] energy level:
[tex]$\begin{aligned}E_4-E_1 & =\frac{h c}{\lambda} \\\lambda & =\frac{\left(6.63 \times 10^{-31}\right) \times\left(3 \times 10^8\right)}{(7-1)\left(1.6 \times 10^{-19}\right)} \mathrm{m} \\& =0.207 \times 10^{-6} \mathrm{~m} \\& \approx 210 \mathrm{~nm}\end{aligned}$[/tex]
(4). Transition of electron from [tex]$E_2$[/tex] to [tex]$E_3$[/tex] energy level:
[tex]$\begin{aligned}E_3-E_2 & =\frac{h c}{\lambda} \\\lambda & =\frac{\left(6.63 \times 10^{-34}\right) \times\left(3 \times 10^8\right)}{(4-2)\left(1.6 \times 10^{-19}\right)} \mathrm{m} \\& =0.621 \times 10^{-6} \mathrm{~m} \\& \approx 620 \mathrm{~nm}\end{aligned}$[/tex]
(5). Transition of electron from[tex]$E_2$[/tex] to [tex]$E_4$[/tex] energy level:
[tex]$\begin{aligned}E_1-E_2 & =\frac{h c}{\lambda} \\\lambda & =\frac{\left(6.63 \times 10^{-34}\right) \times\left(3 \times 10^8\right)}{(7-2)\left(1.6 \times 10^{-19}\right)} \mathrm{m} \\& =0.248 \times 10^{-6} \mathrm{~m} \\& \approx 250 \mathrm{~nm}\end{aligned}$[/tex]
(6). Transition of electron from [tex]$E_3$[/tex] to [tex]$E_4$[/tex] energy level:
[tex]$\begin{aligned}E_4-E_3 & =\frac{h c}{\lambda} \\\lambda & =\frac{\left(6.63 \times 10^{-34}\right) \times\left(3 \times 10^8\right)}{(7-4)\left(1.6 \times 10^{-19}\right)} \mathrm{m} \\& =0.414 \times 10^{-6} \mathrm{~m} \\& \approx 410 \mathrm{~nm}\end{aligned}$[/tex]
Thus, The posslble wavelengths that appear in the emisslon spectrum of the system are[tex]$210 \mathrm{~nm}, 250 \mathrm{~nm}, 410 \mathrm{~nm}, 620 \mathrm{~nm}, 1200 \mathrm{~nm}$[/tex].
Complete question: The allowed energies of a quantum system are 1.0 ev, 2.0 ev, 4.0 ev, and 7.0 ev. what wavelengths appear in the system's emission spectrum
To learn more about wavelengths visit:https://brainly.com/question/13533093
#SPJ4
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.
