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The electirc potential between a proton ...

The electirc potential between a proton and an electron is given by `V = V_0 in (r )/(r_0)` , where r_0 is a constant. Assuming Bhor model to be applicable, write variation of `r_n` with n, being the principal quantum number. (a) `r_n prop n` (b) `r_n prop (1)/(n)` (c ) `r_n^2` (d)`r_n prop (1)/(n^2)`

Text Solution

Verified by Experts

`:. U = eV = eV_0 in ((r )/(r_0))`
`|F| = |-(dU)/(dr)| = (eV_0)(r )`
This force will provide the necessary centripetal force. Hence, `(mv^2)/(r ) = (eV_0)/(r )`
or `v= sqrt(eV_0)/(m)
.....(i) Moreover, ` mur = (nh)/(2pi)
....(ii) Dividing Eq. (ii) by Eq. (i) we have
`mr = ((nh)/(2pi)) sqrt(m)/(eV_0) or r_n prop n`
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Knowledge Check

  • The elecrric potential between a proton and as electron is given by V= V_(0) ln (r /r_(0)) , where r_(0) is a constant . Assuming Bohr's model to be applicable , write variation of r_(n) with n , n being the principal quantum number ?

    A
    `r_(n) prop n `
    B
    `r_(n) prop 1//n `
    C
    `r_(n) prop n^(2)`
    D
    `r_(n) prop 1//n^(2) `
  • The potential of an atom is given by V=V_(0)log_(e)(r//r_(0)) where r_(0) is a constant and r is the radius of the orbit Assumming Bohr's model to be applicable, which variation of r_(n) with n is possible (n being proncipal quantum number)?

    A
    `r_(n)oon`
    B
    `r_(n)1//oon`
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    `r_(n)oon^(2)`
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    `r_(n)1//n^(2)`
  • The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

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    C
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    D
    `-n^2+4n`
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