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If a proton had a radius R and the charg...

If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i)`R=0.1Å`, and (ii)`R=10Å`

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To calculate the ground state energy of a hydrogen atom with a uniformly distributed charge on the proton using Bohr's theory, we can follow these steps: ### Step 1: Understand the Formula The ground state energy \( E \) of a hydrogen atom in Bohr's model is given by the formula: \[ E = -\frac{Z e^2}{8 \pi \epsilon_0 r} \] where: ...
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Knowledge Check

  • If a proton had a radius R and the charge was uniformaly fistributed , Calculate using bohr theory, the ground state energy of a H-atom When R=10Å

    A
    `-13.6eV`
    B
    `-0.68eV`
    C
    `-0.72eV`
    D
    `-1.51eV`

  • If a proton had a radius R and the chrge was uniformaly distributed, the ground state energy (ineV) of a H -atom for R=0.1Å is

    A
    `-13.6`
    B
    `-27.2`
    C
    `-3.4`
    D
    `-30.8`

  • If R is the Rydberg's constant, the energy of an electron in the ground state H atom is

    A
    `(Rc)/h`
    B
    `(-1)/(Rhc)`
    C
    `-Rhc`
    D
    `(vc)/R`

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    The Bohr model for the H-atom relies on the Coulomb's law of electrostatics. Coulomb's law has not directly been verified for very short distances of the order of angstroms. Supposing Coulomb's law between two opposite charge +q_(1), -q_(2) is modified to |vecF|=(q_(12))/((4piepsilon_(0))) 1/(r^(2)) , rgeR_(0) =(q_(1)q_(2))/((4piepsilon_(0))) 1/(R_(0)^(2)) ((R_(0))/r)^(epsilon) , rleR_(0) Calculate in such a case, the ground state energy of a H-atom, if epsilon=0.1, R_(0)=1Å .

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