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Explain about the shape of orbitals. |
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Answer» Solution :The solution to Schrodinger equation gives the PERMITTED energy values called eigen values and the wave functions corresponding to the eigen values are callled atomic orbitals For 1s orbital,l=0,m=0.f`(theta)`=`(1)/sqrt(2)` and `G(varphi)`=`(1)/(sqrt(2pi))`THerefore,the angular distribution function is equal to `(1)/(2sqrt(pi))`.i.e. it is INDEPENDENT of the ANGLE`theta` and `varphi`.Hence ,the probability of finding the electron is independent of the direction from the nucleus.So,the shape of the s orbital is spherical. ,p-orbital: For p orbitals l=1 and the corresponding m values are-1,0 and +1 . The THREE different m values indicated that there are three different orientations possible for p orbitals,These orbitals are designated as `p_x,p-y` and `p_z`,The shape of p orbitals are dumb bell shape. , D-orbital: For.d. orbital l=2 and the corresponding m values are -2,-1,0,=1,+2. the shape of the d orbital looks like a .clover leaf..The five m values give rise to five d orbitals namely`d_(xy),d_(yz),d_(zx),d_(x^(2)-y^(2))` and `d_z^(2)`.The 3d orbitals contain two nodel planes. ,f-orbitals: For .f. orbitals,l=3 and mvalues are -3,-2,-1,0,+1,+2,+3 corresponding to seven f orbitals `fz^(3),f_(xz^(2)),f_(yz^(2)),f_(xyz),f_(z(x^(2)-y^(2)),f_(x(x^(2)-3y^(2)),f_(y(3x^(2)-y^(2))`.They contain 3 nodal planes.
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