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How many times dies the electon go round...

How many times dies the electon go round the first Bohr`s orbit of hydrogen in one second ?

Text Solution

Verified by Experts

For H-atom : `u_1 = ( 2pie^2)/h , r_1 = h^2 /(4 pi^2 me^2)`
` therefore` Circumference fo I Bohr orbit ` = 2 pi r_1`
` = ( 2 pi h^2 )/( 4 pi me^2) = h^(2)/(2pime^(2))` ` therefore` No . of round by electron in I orbit
` = u_1 /(2 pir_1) =( 2 pe^2 xx 2 pi me^2) /(hxx h^2) = ( 4 pi^2me^4)/(h^3)`
` = 4 xx (3 . 14 )^2 xx 9.108 xx 10^(-28) xx ((4. 803 xx 10^(-10))^4)/((6.626 xx 10^(-27)))^3`
`= 6.57 xx 10^(15)`.
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Knowledge Check

  • The kinetic energy of electron in the first Bohr orbit of the hydrogen atom is

    A
    `-6.5 eV`
    B
    `-27.2 eV`
    C
    `13.6 eV`
    D
    `-13.6 eV`
  • What is the orbital acceleration of the electron in the first bohr orbit of hydrogen atom ?

    A
    `(h)/(2pi^2m^2r^3)`
    B
    `(h^2)/(2pi^2m^2r^2)`
    C
    `(h^2)/(4pi^2m^2r^3)`
    D
    `(h^3)/(4pi^2m^2 r^2)`
  • The number of revolutions per second made by an electron in the first Bohr orbit of hydrogen atom is of the order of 3 :

    A
    `10^(20)`
    B
    `10^(19)`
    C
    `10^(17)`
    D
    `10^(15)`
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