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N^(th) level of Li^(2+) has the same ene...

`N^(th)` level of `Li^(2+)` has the same energy as the ground state energy of the hydrogen atom. If `r_(N)` and `r_(1)` be the radius of the `N^(th)` Bohr orbit of `Li^(2+)` and first orbit radius of H atom respectively, then the ratio `(r_(N))/(r_(1))` is

A

9

B

`1//9`

C

3

D

None

Text Solution

Verified by Experts

The correct Answer is:
C
`E=(E_(0)Z^(2))/(n^(2))=E_(0)rArr n=Z=3, ` for Lithium ` r=(r_(0)n^(2))/(Z)=(r_(0).3^(2))/(3)=3r_(0)`
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Knowledge Check

  • The energy of an electron in n^"th" orbit of hydrogen atom is

    A
    `13.6/n^4 eV`
    B
    `13.6/n^3 eV`
    C
    `13.6/n^2 eV`
    D
    `13.6/n` eV

  • If the radius of 2nd Bohr orbit of hydrogen atoms is r_(2) . The radius of third Bohr orbit will be

    A
    `4/9r_(2)`
    B
    `4r_(2)`
    C
    `9/4r_(2)`
    D
    `9r_(2)`

  • If the radius of the first Bohr orbit of the H atom is r then for the Li^(2+) ion it will be:

    A
    `3r`
    B
    `9r`
    C
    `r//3`
    D
    `r//9`

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