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Calcultte the enrgy required for the pro...

Calcultte the enrgy required for the process ,
` He^+ (g) rarr He^(2+) (g) + e`
The ionization energy for the H-atom in the grounds state is ` 2. 18 xx 10 ^(-18) J "atom"^(-1)`.

Text Solution

Verified by Experts

For H-like particles, `E_(n) = - (2pi^(2) m Z^(2) e^(4))/(n^(2) h^(2))`
For H-atom, I.E. `= E_(oo) - E_(1) = 0 - (-(2pi^(2) me^(4))/(1^(2) xx h^(2))) = (2pi^(2) me^(4))/(h^(2)) = 2.18 xx 10^9-18) J "atom"^(-1)` (Given)
For the given process,
Energy required `= E_(oo) - E_(1) = 0 = (-(2pi^(2) m xx 2^(2) xx e^(4))/(1^(2) xx h^(2))) = 4 xx (2pi^(2) me^(4))/(h^(2)) = 4 xx 2.18 xx 10^(-18) J`
`= 8.72 xx 10^(-18) J`
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Calculate the energy required for the process He^(+) (g) to He^(2+) (g) + e^(-) The ionization energy for the H atom in the ground state is 2.18 xx 10^(-18) J "atom"^(-1)

The energy needed for Li_(g) rarr Li_(g)^(3+) + 3e is 1. 96 xx 10^4 kJ mol ^(-1) . If the first ionisation energy of Li is 520 k J mol^(-1) . Calcuate the second ionisation energy of Li . (Given : IE_1 for H = 2 . 2. 18 xx 10^(-18) k J "atom"^(-1) ).

Knowledge Check

  • What is the energy required for the process He^+(g)rarrHe^+(g)+e^- if the ionisation energy for H-atom in the ground state is 2.18xx10^-18 J/atom

    A
    `2.18xx10^-18J`
    B
    `13.13xx10^5 J`
    C
    `8.72X 10^-18 J`
    D
    `2626XX 10^5 J`

  • The frequency of the radiation emitted when the electron falls from n = 4 to n = 1 in a hydrogen atom will be (Given ionization energy of H = 2.18 xx 10^(-18) J "atom"^(-1) and h = 6.625 xx 10^(-34) Js )

    A
    `1.54 xx 10^(15) s^(-1)`
    B
    `1.03 xx 10^(15) s^(-1)`
    C
    `3.08 xx 10^(15) s^(-1)`
    D
    `2.0 xx 10^(15) s^(-1)`

  • The total energy of the electron of H-atom in the second quantum state is -E_(2) . The total energy of the He^(+) atom in the third quantum state is:

    A
    `-((3)/(2))E_(2)`
    B
    `-((2)/(3))E_(2)`
    C
    `-((4)/(9))E_(2)`
    D
    `-((16)/(9))E_(2)`

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