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In hydrogen and hydrogen-like atom , the...

In hydrogen and hydrogen-like atom , the ratio of `E_(4 n) - E_(2 n) and E_(2 n) - E_(n)` varies with atomic nimber `z` and principal quantum number`n` as

A

`z^(2)//n^(2)`

B

`z^(4)//n^(4)`

C

`z//n`

D

`(n^(2)//z^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`E_(n)= -13.6/n^(2) (Z^(2))`
`E_(2n)= -13.6/((2n)^(2)) Z^(2)=13.6/4 (Z^(2)/n^(2))`
`E_(2n)-E_(n)=[(-13.6/4)Z^(2)/n^(2)]-[-3.6 (Z^(2)/n^(2))]`
`E_(2n)-E_(n)= -(13.6 )/(4) Z^(2)/n^(2)+13.6 Z^(2)/n^(2)`
`E_(2n)-E_(n)=Z^(2)/n^(2) (13.6-13.6/4)=(10.2) (Z^(2)/n^(2))`
`(E_(2n))(E_(n))=((13.6)^(2))/(4) (Z^(4)/n^(4))`
`((E_(2n)-E_(n)))/((E_(2n))(E_(n)))=((10.2)(Z^(2)/n^(2)))/(((13.6)^(2))/4 (Z^(4)/n^(4))) implies ((E_(2n)-E_(n)))/((E_(2n))(E_(n))) prop (n^(2)/Z^(2))`
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Knowledge Check

  • In hydrogen and hydrogen like atoms, the ratio of difference of energies E_4n-E_2n and E_2n-E_n varies with its atomic number Z and n as

    A
    `Z^2/n^2`
    B
    `Z^4/n^4`
    C
    `Z/n`
    D
    `Z_0n_0`

  • The ratio of E _(2) - E_(1) to E_(4) - E_(3) for the hydrogen atom is approximately equal to -

    A
    10
    B
    15
    C
    17
    D
    12

  • According to the Bohr theory of Hydrogen atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as

    A
    `(1)/(n), (1)/(n^(2)), n^(2)`
    B
    `(1)/(n), n^(2), (1)/(n^(2))`
    C
    `n^(2), (1)/(n^(2)), n^(2)`
    D
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