B2. Using Bohr's theory, obtain an expression for the radius of the electron orbital. Calculate the radius of the orbital nearest to the nucleus in a hydrogen atom.

Bohr's theory of the atom postulates that electrons orbit the nucleus in discrete energy levels, with each level corresponding to a specific radius. The expression for the pi * m * E)<br /><br />where:<br />r is the radius of the electron orbital,<br />n is the principal quantum number (which represents the energy level of the electron),<br />h is the Planck constant,<br />m is the mass of the electron, and<br />E is the energy of the electron.<br /><br />To calculate the radius of the orbital nearest to the nucleus in a hydrogen atom, we can use the formula with n = 1 (since it is the orbital closest to the nucleus). The Planck constant (h) is approximately 6.626 x 10^-34 J*s, and the mass of the electron (m) is approximately 9.109 x 10^-31 kg. The energy of the electron in the ground state of a hydrogen atom is approximately -13.6 eV, which we can convert to joules by multiplying by the charge of the electron (1.602 x in a hydrogen atom:<br /><br />r = (1)^2 * (6.626 x 10^-34 J*s) / (2 * pi * (9.109 x 10^-31 kg) * (-13.6 eV * 1.602 x 10^-19 C / 1.6 x 10^-19 J))<br /><br />r = 5.29 x 10^-11 m<br /><br />Therefore, the radius of the orbital nearest to the nucleus in a hydrogen atom is approximately 5.29 x 10^-11 meters.