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The energies of an electron in first or...

The energies of an electron in first orbit `He ^(+)` and in third orbit of ` Li^(2+) ` in J are respectively

A

`- 872xx10^(-18), - 2.18 xx10^(-18)`

B

`- 872xx10^(-18), - 1.96 xx10 ^(-17)`

C

`-1.96 xx10^(-17), - 2.18 xx 10^(-18)`

D

`- 8.72xx10^(-17), - 1.96 xx 10^(-17)`

Text Solution

Verified by Experts

The correct Answer is:
A
Key Idea Use relation:
` E_(n) = - 2.18 xx10 ^(-18) .(Z^(2))/(n^(n)) J//ion`
where,
` E_(n) `= energy of an electron in nth orbit
Z = atmic number , n = ortit number
For helium ion ` (He^(+))`
Z = 2 , n = 1
` therefore E_(n) = - 2.18 xx 10^(-18) xx (2^(2))/(1^(2))`
` = -8.72 xx 10^(-18) J`
For lithium ion ` (Li^(2+))`
Z = 3 , n = 3
` therefore E_(n) = - 2.18 xx 10^(-18) xx (3^(2))/(3^(2))`
` = - 218 xx 10^(-18) J`
Hence, option (a) is the correct answer .
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Knowledge Check

  • Energy of an electron in nth Bohr orbit is given as

    A
    `-(n^2 h^2)/(4pi^2 mZe^2)`
    B
    `-(2pi^2 Z^2 me^4)/(n^2 h^2)`
    C
    `-(2pi Ze^2)/(nh)`
    D
    `-(n^2 h^2)/(2pi^2 Z^2 me^4)`

  • Energy of an electron in n^(th) Bohr orbit is given as

    A
    `-(n^(2)h^(2))/(4pi^(2)m Ze^(2))`
    B
    `-(2n^(2)Z^(2) m e^(4))/(n^(2)h^(2))`
    C
    `-(2pi Ze^(2))/(nh)`
    D
    `-(n^(2)h^(2))/(2pi^(2)Z^(2) m e^(4))`

  • Energy of an electron in n^(th) Bohr orbit is given as

    A
    `-(n^(2)h^(2))/(4pi^(2)mZe^(2))`
    B
    `-(2pi^(2)Z^(2)me^(4))/(n^(2)h^(2))`
    C
    `-(2piZe^(2))/(nh)`
    D
    `-(n^(2)h^(2))/(2pi^(2)Z^(2)me^(4))`

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