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Separation energy of a hydrogen like ion...

Separation energy of a hydrogen like ion from its third excited state is 2.25 times the separation energy of hydrogen atom from its first excited state. Find out the atomic number of this hydrogen like ion.

Text Solution

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The correct Answer is:
3
Let the separation energy of the ion in third excited state (n=4) be E. Then `E=13.6 xx Z^(2) xx (1)/(16) eV` and in the first excited state
`(n=2),E_(H)=13.6 xx (1)/(4) eV` `implies(E)/(E_(H))=Z^(2) xx (4)/(16)` `implies(2.25 E_(H))/(E_(H))=(Z^(2))/(4)` `impliesZ^(2)=9` `implies Z=3`
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Knowledge Check

  • The ratio of energies of hydrogen atom in its first excited state to third excited state is

    A
    `1/4`
    B
    `4/1`
    C
    `3/4`
    D
    `4/3`

  • the energy required to excite an electron in hydrogen atom to its first excited state is

    A
    `8.5eV`
    B
    `10.2eV`
    C
    `12.7eV`
    D
    `13.6eV`

  • The ratio of the energies of the hydrogen atom in its first to second excited state is

    A
    `1//4`
    B
    `4//9`
    C
    `9//4`
    D
    `4`

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