Quantum Chemistry/Example 19

==Write an example question showing the calculation of the frequency of EM radiation required to excite an H atom from ground to n=2 electronic state.==

The energy of the hydrogen atom is calculated using the following equation:

'''Energy of Hydrogen Atom''' $E=-\left(\frac{m_e{e}^4}{32{\pi }^2{ϵ}_0^2{h}^2}\right)\frac{1}{n^2}$

Template:BookCatTo calculate the change in energy required to go from the ground state to n=2, the following equation is used:

$\delta E=-\left(\frac{m_e{e}^4}{32{\pi }^2{ϵ}_0^2{h}^2}\right)\frac{1}{n^2}+\left(\frac{m_e{e}^4}{32{\pi }^2{ϵ}_0^2{h}^2}\right)\frac{1}{n^2}$

$\delta E=-\left(\frac{m_e{e}^4}{32{\pi }^2{ϵ}_0^2{h}^2}\right)\frac{1}{4}+\left(\frac{m_e{e}^4}{32{\pi }^2{ϵ}_0^2{h}^2}\right)\frac{1}{1}$

$\delta E=\left(\frac{m_e{e}^4}{32{\pi }^2{ϵ}_0^2{h}^2}\right)\frac{5}{4}$

$\delta E=\left(\frac{(9.10938x10{)}^{-31}kg(1.60218x10^{-19}c{)}^4}{32{\pi }^{2}8.854x10^{1}2c^2{S}^2/kg{m}^2{)}^2(1.054x10^{-24}J.s{)}^2}\right)\frac{5}{4}$

$\delta E=\left(\frac{(9.10938x10{)}^{-31}kg(1.60218x10^{-19}c{)}^4}{32{\pi }^{2}8.854x10^{1}2c^2{S}^2/kg{m}^2{)}^2(1.054x10^{-24}J.s{)}^2}\right)\frac{5}{4}$

δE =((9.10938x10)−31kg(1.60218x10−19c)432π28.854x1012c2S2/kgm2)2(1.054x10−24J.s)2)54