F=(1)/(4 pi E_(0))*(q_(1)^(0)h_(2))/(sigma^(2))

The vector form of Coulomb's law is (A) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3))vec r (B) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3)) (C) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(2))vec r (D) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r)vec r

The vector form of Coulomb's law is (A) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3))vec r (B) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(3)) (C) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(2))vec r (D) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r)vec r

The electric force between two electric charges is given by F= (1)/(4pi epsi_(0))(q_(1)q_(2))/(r^(2)) . where is a distance . between charges q_(1) and q_(2) . So, unit and dimensional formula of epsi_(0) , is ...... and...... respectively.

The Bohr model for the H-atom relies on the Coulomb's law of electrostatics. Coulomb's law has not directly been verified for very short distances of the order of angstroms. Supposing Coulomb's law between two opposite charge +q_(1),-q_(2) is modified to |F|=(q_(2)q_(1))/((4pi epsi_(0)))(1)/(r^(2)),r ge R_(0) =(q_(1)q_(2))/(4pi epsi_(0))(1)/(R_(0)^(2))((R_(0))/(r))^(e),r lt R_(0) Calculate in such a case, the ground state energy of a H-atom if epsi=0.1 R_(0)=1Å

The wave function of 3s and 3p_(z) orbitals are given by : Psi_(3s) = 1/(9sqrt3) ((1)/(4pi))^(1//2) ((Z)/(sigma_(0)))^(3//2)(6=6sigma+sigma)e^(-sigma//2) Psi_(3s_(z))=1/(9sqrt6)((3)/(4pi))^(1//2)((Z)/(sigma_(0)))^(3//2)(4-sigma)sigmae^(-sigma//2)cos0, sigma=(2Zr)/(nalpha_(0)) where alpha_(0)=1st Bohr radius , Z= charge number of nucleus, r= distance from nucleus. From this we can conclude:

The wave function of 3s and 3p_(z) orbitals are given by : Psi_(3s) = 1/(9sqrt3) ((1)/(4pi))^(1//2) ((Z)/(sigma_(0)))^(3//2)(6-6sigma+sigma)e^(-sigma//2) Psi_(3p_(z))=1/(9sqrt6)((3)/(4pi))^(1//2)((Z)/(sigma_(0)))^(3//2)(4-sigma)sigmae^(-sigma//2)cos0, sigma=(2Zr)/(nalpha_(0)) where alpha_(0)=1st Bohr radius , Z= charge number of nucleus, r= distance from nucleus. From this we can conclude:

For H-atom wave function for a particulaonstate is: Psi=(1)/(81sqrt(3pi))((1)/(a_(0)))^(3//2) (sigma^(2)-10sigma+25)e Where sigma=r//a_(0) and a_(0) is Bohr's radius (0.53overset(@)A) . Then distance of farthest radius mode is approximately.

The electric field at point P due to a charged ball is given by E_(p)=(1)/( 4pi epsilon_(0))(q)/(r^(2)) To measure 'E' at point P, A test charge q_(0) is placed at point P and measure electric force F upon the test charge. Check whether (F)/(q_(0)) is equal to (1)/(4pi epsilon_(0))(q)/(r^(2)) or not .