91Ó°ÊÓ

The given hydronics are${\mathrm{O}}^{-7}$

$Wecanbeginbyexpres\sin genergylevelsasfollows:\$\$\backslash begin\left\{aligned\right\}E\_\left\{n\right\}\&=-\backslash frac\{13.6Z^\{2\left\}\right(eV\left)\right\}\{n^\{2\left\}\right\}E\_\left\{3\right\}-E\_\left\{2\right\}=-13.6Z^\left\{2\right\}(eV)\backslash cdot\backslash left(\backslash frac\{1\left\}\right\{3^\left\{2\right\}\}-\backslash frac\{1\left\}\right\{2^\left\{2\right\}\}\backslash right)\backslash \backslash E\_\left\{3\right\}-E\_\left\{2\right\}=\backslash frac\{hc\}\{\backslash lambda\_\{32\left\}\right\}\backslash \backslash \backslash lambda\_\left\{32\right\}=\backslash frac\{hc\}\left\{E\_\right\{3\}-E\_\{2\left\}\right\}\backslash \backslash \backslash lambda\_\left\{32\right\}=\backslash frac\{-13.6\backslash cdot8^\{2\}\backslash cdot1.6\backslash cdot10^\{-19\}\backslash cdot\backslash left(\backslash frac\left\{1\right\}\{3^\{2\left\}\right\}-\backslash frac\left\{1\right\}\{2^\{2\left\}\right\}\backslash right\left)\right\}\{10.26\backslash mathrm\{~nm\left\}\right\}\backslash \backslash \backslash lambda\_\left\{32\right\}\&=10^\{-34\}\backslash cdot3\backslash cdot10^\left\{8\right\}\backslash end\left\{aligned\right\}Wecanbeginbyexpres\sin genergylevelsasfollows:\$\$\backslash begin\left\{aligned\right\}E\_\left\{n\right\}\&=-\backslash frac\{13.6Z^\{2\left\}\right(eV\left)\right\}\{n^\{2\left\}\right\}E\_\left\{3\right\}-E\_\left\{2\right\}=-13.6Z^\left\{2\right\}(eV)\backslash cdot\backslash left(\backslash frac\{1\left\}\right\{3^\left\{2\right\}\}-\backslash frac\{1\left\}\right\{2^\left\{2\right\}\}\backslash right)\backslash \backslash E\_\left\{3\right\}-E\_\left\{2\right\}=\backslash frac\{hc\}\{\backslash lambda\_\{32\left\}\right\}\backslash \backslash \backslash lambda\_\left\{32\right\}=\backslash frac\{hc\}\left\{E\_\right\{3\}-E\_\{2\left\}\right\}\backslash \backslash \backslash lambda\_\left\{32\right\}=\backslash frac\{-13.6\backslash cdot8^\{2\}\backslash cdot1.6\backslash cdot10^\{-19\}\backslash cdot\backslash left(\backslash frac\left\{1\right\}\{3^\{2\left\}\right\}-\backslash frac\left\{1\right\}\{2^\{2\left\}\right\}\backslash right\left)\right\}\{10.26\backslash mathrm\{~nm\left\}\right\}\backslash \backslash \backslash lambda\_\left\{32\right\}\&=10^\{-34\}\backslash cdot3\backslash cdot10^\left\{8\right\}\backslash end\left\{aligned\right\}$uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('d5333838ebe0bea...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage('

$E_n=-\frac{13.6Z^2\left(eV\right)}{n^2}$$E_3-E_2=-13.6Z^2\left(eV\right)·\left(\frac{1}{3^2}-\frac{1}{2^2}\right)$

$E_3-E_2=\frac{hc}{{\mathrm{λ}}_{32}}$

$$\begin{gathered} {\mathrm{λ}}_{32}=\frac{hc}{E_3-E_2} \\ {\mathrm{λ}}_{32}=\frac{-13.6·8^2·1.6·{10}^{-19}·\left(\frac{1}{3^2}-\frac{1}{2^2}\right)}{10.26\mathrm{nm}} \\ {\mathrm{λ}}_{32}={10}^{-34}·3·{10}^8 \end{gathered}$$

In the same approach, we can determine out $4→2$and $5→2$transitions:

$$\begin{gathered} {\mathrm{λ}}_{42}=\frac{hc}{E_4-E_2} \\ {\mathrm{λ}}_{42}=\frac{6.63·{10}^{-34}·3·{10}^8}{-13.6·8^2·1.6·{10}^{-19}·\left(\frac{1}{4^2}-\frac{1}{2^2}\right)} \end{gathered}$$

$$\begin{gathered} {\mathrm{λ}}_{42}=7.6\mathrm{nm} \\ {\mathrm{λ}}_{52}=\frac{hc}{E_5-E_2} \\ {\mathrm{λ}}_{52}=\frac{6.63·{10}^{-34}·3·{10}^8}{-13.6·8^2·1.6·{10}^{-19}·\left(\frac{1}{5^2}-\frac{1}{2^2}\right)} \\ {\mathrm{λ}}_{52}=6.79\mathrm{nm} \end{gathered}$$