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ntoOrbit no , zto Atomic no implies r(n....

`nto`Orbit no , `zto` Atomic no `implies r_(n.z)to` Radius `v_(n.z)to` Velocity
`T_(n.z)to` Time period of Revolution `implies K_(n.z)to` kinetic energy of the electron
`{:("Column-I","Column-II"),("(for single electron species)","(Ratio)"),((A)r_(2,1):r_(1,2),(P)"9:1"),((B)V_(1,3):V_(3,1),(Q)"8:1"),((C )T_(1,2):T_(2,1),(R)"16:1"),((D)K_(1,2):K_(2,1),(S) "1:32"):}`

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The correct Answer is:
A`to`Q ; B`to`P ; C`to`S ,D`to`R

(i)`r=0.521xxn^2/z A^@` , (ii)`V=2.18xx10^6 z//n` , (iii)`T prop n^3//z^2` , (iv)`K.E prop z^2/n^2`
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In Bohr's model, r_(n,z)= radius of n^(th) orbit with atomic number Z u_(n,z) =P.E of electron in n^(th) orbit with atomic number Z K_(n,z) = K.E of electron in n^(th) orbit with atomic number Z V_(n,z) = velocity of electron in n^(th) orbit with atomic number Z T_(n,z)= time period of revolution in n^(th) orbit with atomic number Z {:(Column I,Column II),((A)U_(1.2),K_(1.1),(p)1:8),((B)r_(2.1),r_(1.2),(q)-8:1),((C)V_(1.3),V_(3.1),(r)9:1),((D)T_(1.2),T_(2.2),(s)8:1):}

Frequancy =f_(1) , Time period = T, Energy of n^(th) orbit = E_(n) , radius of n^(th) orbit =r^(n) , Atomic number = Z, Orbit number = n : {:(,"Column-I",,"Column-II",),((A),f,(p),n^(3),),((B),T,(q),Z^(2),),((E),E_(n),(r ),(1)/(n^(2)),),((D),(1)/(r_(n)),(s),Z,):}

Let R_(t) represents activity of a sample at an insant and N_(t) represent number of active nuclei in the sample at the instant. T_(1//2) represents the half life. {:(,"Column I",,"Column II"),((A),t=T_(1//2),(p),R_(t)=(R_(0))/(2)),((B),t=(T_(1//2))/(ln2),(q),N_(0)-N_(t)=(N_(0))/(2)),((C),t=(3)/(2)T_(1//2),(r),(R_(t)-R_(0))/(R_(0)) = (1-e)/(e)),(,,(s),N_(t)=(N_(0))/(2sqrt(2))):}

If in Bohr's model, for unielectronic atom, time period of revolution is represented as T_(n,z) where n represents shell no. and Z represents atomic number then the value of T_(1,2):T_(2,1) , will be :

If in Bohr's model, for unielectronic atom, time period of revolution is represented as T_(n,z) where n represents shell no. and z represents atomic number then the value of T_(1.2) : T_(2.1) will be :-

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