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For an electron in a hydrogen atom, the ...

For an electron in a hydrogen atom, the wave function y is proportional to exp-`r//a_(0)`, where `a_(0)` is the Bohr radius. Find the ratio of probability of finding the electron at the nucleus to the probability of finding it at `a_(0)`.

Text Solution

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Probability of finding the electron at `s=a_(0)` is proportional to `e^(-2s//a_(0)=e^(-2)`
Since `P= |Psi|^(2) prop (e ^(-s//a_(0)))^(2)`, probability at nucleus = 0
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For an electron in a hydrogen atom, the wave function psi is proportional to exp -r//a_(0) , where a_(0) is the Bohr radius. Find the ratio of probability of finding the electron at the nucleus to the probability of finding it at a_(0) .

Represent graphically, the variation of probability density (psi^2 _(r)) as a function of distance (r ) of the electron from the nucleus for 1s and 2s orbitals.

Knowledge Check

  • The radius of the first Bohr orbit of hydrogen atom is 0.529Å . The radius of the third orbit of H^(+) will be

    A
    a)`8.46Å`
    B
    b)`0.705Å`
    C
    c)`1.59Å`
    D
    d) 4.29Å`

  • Electrons of energies 10.26 eV and 12.09 eV can cause radiations to be emitted from hydrogen atoms. Find the maximum wavelength of the radiations if the electrons drop back to the ground state.

    A
    `1206Å`
    B
    `1020Å`
    C
    `1495Å`
    D
    `1617Å`

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