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)where:r is the radius of the electron orbital,n is the principal quantum number (which represents the energy level of the electron),h is the Planck constant,m is the mass of the electron, andE is the energy of the electron.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: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))r = 5.29 x 10^-11 mTherefore, the radius of the orbital nearest to the nucleus in a hydrogen atom is approximately 5.29 x 10^-11 meters.