What is the ratio of the time periods of an electron in the $n = 2$ and $n = 1$ orbits of a hydrogen atom (in $:1$)?

  • A
    $2$
  • B
    $4$
  • C
    $8$
  • D
    $16$

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In a hypothetical Bohr hydrogen atom,the mass of the electron is doubled. The energy $E_0$ and the radius $r_0$ of the first orbit will be ($a_0$ is the Bohr radius).

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is $...... \text{ } \mathring{A}$ (radius of the first orbit of hydrogen atom $= 0.53 \text{ } \mathring{A}$).

In Bohr's atomic model,the electron is assumed to revolve in a circular orbit of radius $0.5 \times 10^{-10} \; m$. If the speed of the electron is $2.2 \times 10^{6} \; m/s$,then the current associated with the electron will be $.... \times 10^{-2} \; mA$. [Take $\pi$ as $\frac{22}{7}$]

The following parameter is the same for all hydrogen-like atoms and ions in their ground state.

The angular momentum of an electron in Bohr's hydrogen atom having energy $(-0.544) \text{ eV}$ is ($h$ = Planck's constant)

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