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Write the expression for the radius of n^(th) orbit of the hydrogenic atoms and give the meanings of the symbols used. |
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Answer» SOLUTION :Kinetic energy for the electron `E_(k)=(1)/(2)mv^(2)` But `(mv^(2))/( r)=(1)/(4pi epsi_(0).(Ze^(2))/(r^(2))` `E_(k)=(1)/(2)((1)/(4pi epsi_(0)).(Ze^(2))/ (r ))=(1)/(8pi epsi_(0)).(Ze^(2))/( r )` Potential energy, E = Charge `E_(p)`= Charge `XX` potential `=-exx(1)/(4pi epsi_(0)).(Ze)/(r)=-(1)/(4pi epsi_(0)).(Ze^(2))/(r)` Total energy `E=E_(k)+E_(p)` `=(1)/(8pi epsi_(0)).(Ze^(2))/(r)-(1)/(4pi epsi_(0)).(Ze^(2))/( r )=-(1)/(8pi epsi_(0)).(Ze^(2))/( r )` Butradius `r=(epi_(0)n^(2)h^(2))/(nmZe^(2))` substituting the value the value of r, we get Total energy `T.E.=(-mZ^(2)e^(4))/(8 epsi_(0)^(2)n^(2)h^(2))` |
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