Structure of Atom — Chemistry STD 11 Science — Question
Maharashtra BoardEnglish MediumSTD 11 ScienceChemistryStructure of Atom6 Marks
Question
Write a short note on Schrodinger equation.
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Answer
Schrodinger equation or wave equation:
$i.$ Schrodinger developed the fundamental equation of quantum mechanics which incorporates wave particle duality of matter. The Schrodinger equation or wave equation is written as:
It $\hat{\mathbf{H}} \psi=\mathrm{E} \psi$
Here $\hat{\mathbf{H}}$ is a mathematical operator called Hamiltonian, $\psi ($psi$)$ is the wave function and $\mathrm{E}$ is the total energy of the system.
$ii.$ When Schrodinger equation is solved for an electron in hydrogen atom, the possible values of energy states $(\mathrm{E})$ that the electron may have along with the corresponding wave function $(\psi)$ are obtained. As a consequence of solving this equation, a set of three quantum numbers characteristic of the quantized energy levels and the corresponding wave functions are obtained. These are: Principal quantum number ( $\mathrm{n}$ ), azimuthal quantum number $( \mathrm{I})$ and magnetic quantum number $\left(m_1\right)$.
$iii.$ The solution of Schrodinger wave equation led to three quantum numbers and successfully predicted features of hydrogen atom emission spectrum.
$iv.$ Splitting of spectral lines in multi$-$electron atomic emission spectra could not be explained through such model. These were explained by George Uhlenbeck and Samuel Goudsmit $(1925)$ who proposed the presence of the fourth quantum number called electron spin quantum number, $m_s.$
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