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Explain the formulas of energy of electron in atom revolving around the nucleus in different orbits. |
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Answer» Solution :According to the Rutherford nuclear model of the atom which is a electrical neutral sphere of a very small, massive and positively charged nucleus at the centre surrounding by the revolving electron in their respective STABLE orbits. The electrostatic force of attraction, `F_(e)` between the revolving electrons and the nucleus provides the requisite centripetal force to keep them in their orbits. For a stable orbit in a hydrogen atom, `F_(e)=F_(e)` where `F_(e)=` Electric force `F_(e)=` Centripetal force `:.(1)/(4pi epsi_(0))*(e^(2))/(r^(2))=(MV^(2))/(r)` `:.r=(e^(2))/(4pi epsi_(0)) mv^(2)....(1)` which is the relation between the velocity of electron to the orbital radius. The kinetic energy of electron in hydrogen atom. `(1)/(2)mv^(2)=(e^(2))/(2xx4pi epsi_(theta)r) [ :.`From equqtion (1)] And potential energy `tj=-(1)/(4pi epsi_(0))*(Zexxe)/(r)""..(3)` [ `:.` For hydrogen Z=1] In this formula, the negative sign in U signifies that the electrostatic force is in the -r. Hence, the total energy of electron in a hydrogen atom is, `E=K+U` `=(e^(2))/( 8pi epsi_(0)r)-(e^(2))/(4pi epsi_(0)r)` [ `:.` From EQUATION (1) and (2)] `:.E=(e^(2)-2e^(2))/(8 pi epsi_(0)r)=-(e^(2))/(8 pi epsi_(0)r)` `:. E=-(e^(2))/(8 pi epsi_(0)r)` The total energy of the electron is negative. The implies the fact that the electron is bound to tl nucleus. If total energy were positive, an electron will N follow a closed orbit around the nucleus. |
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