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Prove that velocity v(n) = sqrt((Ze^(2))...

Prove that velocity `v_(n) = sqrt((Ze^(2))/(mr_(n)))` for an electron at distance `r_(n)` from the nucleus, where n is the orbit number, Z is the atomic number, m and e are mass and charge of electron respectively.

Text Solution

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Kinetic energy electron `=1/2"mu"^(2)`
From Bohr.s concept `KE=1/2 (Ze^(2))/(r_(n))`
`1/2"mu"^(2)=1/2(Ze^(2))/(r_(0))`
`:.u=sqrt((Ze^(2))/(mr_(n)))`
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Knowledge Check

  • 7 electrons are in N-orbit of an atom and its nucleus has 18 neutrons. What will be the mass number?

    A
    25
    B
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    C
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    D
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  • If n is the orbit number of the electron in a hydrogen atom, the correct statement among the following is

    A
    electron energy increases as n increases.
    B
    hydrogen emits infrared rays for the electron tranition from `n=prop` to `n=1`.
    C
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    D
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