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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 atom

Monjur Alahi

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]
A. `L_1/L_2=n_1/n_2`
B. `P_1/P_2=(Z_1n_2)/(Z_2n_1)`
C. `f_1/f_2 = (Z_2/Z_1)^2 (n_1/n_2)^3`
D. `((K.E)_1)/((K.E)_2)=(Z_1/Z_2 . n_2/n_1)^2`


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Salim Ahmed Kawsar

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Correct Answer - A,B,D
`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`

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