Electrons are revolving around the nucleus in n_(1^(th)) orbit of an atom, have atomic number Z_1, and in the n_2 orbit of other atom, have atomic number Z_2, then [Where P= Linear momentum, L=Angular momentum, f=frequency of revolution and K.E. =kinetic energy]

Electrons are revolving around the nucleus in n_(1^(th)) orbit of an a

1.	Electrons are revolving around the nucleus in n_(1^(th)) orbit of an atom, have atomic number Z_1, and in the n_2 orbit of other atom, have atomic number Z_2, then [Where P= Linear momentum, L=Angular momentum, f=frequency of revolution and K.E. =kinetic energy]
Answer» `L_1/L_2=n_1/n_2` `P_1/P_2=(Z_1n_2)/(Z_2n_1)` `f_1/f_2=(Z_2/Z_1)^2 (n_1/n_2)^3` `((K.E)_1)/((K.E)_2)=(Z_1/Z_2 . n_2/n_1)^2` SOLUTION :`L_1/L_2=(mv_1r_1)/(mv_2r_2)=(Z_1/n_1xxn_1^2/Z_1)/(Z_2/n_2xxn_2^2/Z_2)=n_1/n_2implies P_1/P_2(mv_1)/(mv_2)=(Z_1/n_1)/(Z_2/n_2)=(Z_1n_2)/(Z_2n_1)` `(f_1)/(f_2) =(v_1/(2pir_1))/(v_2/(2pir_2))=(Z_1/n_1xxZ_1/n_1^2)/(Z_2/n_2xxZ_2/n_2^2)=(Z_1/Z_2)^2.(n_2/n_1)^3implies (K.E._1)/(K.E._2)=(1/2mv_1^2)/(1/2mv_2^2)=(Z_1/Z_2)^2XX(n_2/n_1)^2=((Z_1n_2)/(Z_2n_1))^2` `(K.E_1)/(K.E_2)=(1/2(KZ_1e^2)/r_1)/(1/2(KZ_2e^2)/r_2)=(Z_1/n_1^2.Z_1)/(Z_2.Z_2/n_2^2)=(Z_1/Z_2.n_2/n_1)^2`