Consider a hypothetical one-electron atom, where the nucleus and the electron interact with a force $F=-k r$. Here, $r$ is the distance between the electron and the nucleus, and $k$ is a constant. If this atom is studied using the Bohr model, the electron is assumed to move around the nucleus in selected stable orbits of fixed radii, characterized by quantum number $n$. The radius of the orbiting electron (of mass $m_{\mathrm{e}}$ ) is

• Correct answer
  A

  $\left(\frac{n^2 h^2}{4 \pi^2 k m_{\mathrm{e}}}\right)^{1 / 4}$
• B

  $\left(\frac{n^2 h^2}{4 \pi^2 k m_{\mathrm{e}}}\right)$
• C

  $\left(\frac{n^2 h^2}{4 \pi^2 k m_{\mathrm{e}}}\right)^{1 / 3}$
• D

  $\left(\frac{n^2 h^2}{4 \pi^2 k m_{\mathrm{e}}}\right)^{1 / 2}$

Hence, the correct answer is option: 'A'.