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Magnetic field at the center (at nucleus...

Magnetic field at the center (at nucleus) of the hydrogen like atom `("atomic number" = z)` due to the motion of electron in nth orbit is proporional to

A

`(n^(3))/(z^(5))`

B

`(n^(4))/(z)`

C

`(z^(2))/(n^(3))`

D

`(z^(3))/(n^(5))`

Text Solution

Verified by Experts

The correct Answer is:
D
`B_(n) = (mu_(0)l_(n))/(2 r_(n))`
or `B_(n) prop (l_(n))/(r_(n))`
`prop ((f_(n)))/(r_(n))`
`:. B_(n) prop (v_(n)//r_(n))/((r_n))`
`prop (v_(n))/((r_(n))^(2))`
`prop ((z//n))/((n^(2)//z)^(2))`
`prop (z^(3))/(n^(5))`
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Knowledge Check

  • According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n^(th) orbit is proportional to : (n = principal quantum number)

    A
    `n^(-3)`
    B
    `n^(-2)`
    C
    `n^(-4)`
    D
    `n^(-5)`

  • Magnetic moment due to the motion of the electron in nth energy of hydrogen atom is proportional to

    A
    n
    B
    `n^(0)`
    C
    `n^(5)`
    D
    `n^(3)`

  • In Bohr's model of hydrogen atom, the total energy of the electron in nth discrete orbit is proportional to

    A
    n
    B
    `1/n`
    C
    `n^(2)`
    D
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