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Bohr proposed his atomic model based on Planck.s quantum theory and derived following relations for one electron system in C.G.S. units : For H -atom : `r_(n) = n^(2) xx r_(1), E_(n) = E_(1) xx Z^(2), u_(n) = (u_(1))/(n), u_(1) = 2.19 xx 10^(8) cm//sec., E_(1) = -13.6eV`
For 1 electron system, other than H `r_(n) = (n^(2) xx r_(1H))/(Z), E_(N) = (E_(1H) xx Z^(2))/(n^(2)), u_(n) = (u_(1H) xx Z)/(n)`. Later on de Broglie proposed the dual nature of electron and put forward his wave concept. The wave length of electron in an orbit was given `lambda` = h/mu
The circumference (in m) of `3^(rd)` Bohr orbit in H-atom is :

A

`3.0 xx 10^(-7)`

B

`3.0 xx 10^(-8)`

C

`3.0 xx 10^(-6)`

D

`3.0 xx 10^(-9)`

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • Bohr proposed his atomic model based on Planck.s quantum theory and derived following relations for one electron system in C.G.S. units : For H -atom : r_(n) = n^(2) xx r_(1), E_(n) = E_(1) xx Z^(2), u_(n) = (u_(1))/(n), u_(1) = 2.19 xx 10^(8) cm//sec., E_(1) = -13.6eV For 1 electron system, other than H r_(n) = (n^(2) xx r_(1H))/(Z), E_(N) = (E_(1H) xx Z^(2))/(n^(2)), u_(n) = (u_(1H) xx Z)/(n) . Later on de Broglie proposed the dual nature of electron and put forward his wave concept. The wave length of electron in an orbit was given lambda = h/mu The potential energy of electron in 3^(rd) Bohr orbit of H-atom is :

    A
    `-242 xx 10^(-12)` erg
    B
    `-4.84 xx 10^(-12)` erg
    C
    `+4.84 xx 10^(-12)` erg
    D
    `+2.42 xx 10^(-12)` erg

  • If sum _(r=1)^(n) t_(r) = (1)/( 12) n (n+1) (n+2) then sum_(r=1)^(n) (1)/( t_r)

    A
    `(2n)/( n+1)`
    B
    `(4n)/( n+1)`
    C
    `(3n)/( n+2)`
    D
    `(3n)/( n+1)`

  • For which of the following species, the expression for the energy of electron in n^(th) orbit [E_(n) = -(13.6)/(n^(2)) xx Z^(2) e "V atom"^(-1)] has the validity ?

    A
    Tritium
    B
    `Li^(2+)`
    C
    Deuterium
    D
    `He^(2+)`

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