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Calculate the radius and velocity of the...

Calculate the radius and velocity of the electron in the `n^(th)` orbit in hydrogen atom from the following data `e=1.6xx10^(-19)C, m = 9.11 xx10^(-31) , h = 6.625xx10^(-34) JS, epsilon_(0) = 8.85xx10^(-12) " Fm "^(-1) and c = 3 xx10^(8) ms^(-1)`

Text Solution

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Given `e=1.6xx10^(-19)C, m = 9.11 xx10^(-31)kg, h = 6.625xx10^(-34) JS, epsilon_(0) = 8.85xx10^(-12) " Fm "^(-1) and c = 3 xx10^(8) ms^(-1)`
Radius `r_(n)=(epsilon_(0)n^(2)h^(2))/(pime^(2))`
`n^(2)xx((6.625xx10^(-34))^(2)(8.85xx10^(-12)))/(pixx(9.11xx10^(-31))(1.6xx10^(-19)))=5.3xx10^(-11)n^(2)m` ,
`v_(n)=(e^(2))/(2nhepsilon_(0))=((1.6xx10^(-19)))/(2n(6.625xx10^(-34))(8.85xx10^(-12)))=(2.18xx10^(6))/(n)ms^(-1)`
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Calculate the value of Rydberg's constant given m=9.1xx10^(-31) kg, e = 1.6 xx10^(-19)c, epsilon _(0) = 8.854xx10^(-12) Fm^(-1) , c = 3 xx10^(8)ms^(-1),h=6.625xx10^(-34)Js.

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Knowledge Check

  • The radius of the first orbit of electron in hydrogen atom (e=1.6xx10^(-19)" coulomb,

    A
    `53Å`
    B
    `0.53Å`
    C
    `5.3Å`
    D
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  • The radius of the smallest electron orbit in the hydrogen like atom is (0.51xx10^(-10))/4 m, then it is :

    A
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    B
    `He^(+)`
    C
    `Li^(++)`
    D
    `Br^(+++)`

  • What is the wavelength associated with an electron moving with a velocity of 10_6 m/s ? (given h = 6.63 xx 10^(-34) js and m = 9.11 xx 10^(-31) kg)

    A
    7.27nm
    B
    0.727nm
    C
    72.7nm
    D
    none of these.

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