Section A
Q1. (a) Determine the size of the hydrogen atom using uncertainty principle. Given that the potential energy of electron V = (-e2)/(4π\varepsilon0 a), where a is the distance of the electron from the nucleus. (b) Calculate the group and phase velocities for the wave packet corresponding to a relativistic particle. (c) Calculate [Jx2, Jy], [Jz2, Jy] and [J2, Jy], and then show that \langle J, m | Jx2 | J, m \rangle = \langle J, m | Jy2 | J, m \rangle. (d) Calculate the possible angles between \vecL and \vecS for a d-electron in one-electron atom. (e) The force constant of the bond in CO molecule is 1900 N m-1. Calculate the energy of the lowest vibrational level. The reduced mass of CO molecule is 1.14 × 10-26 kg. Given h = 6.63 × 10-34 J s and 1 eV = 1.6 × 10-19 J.
(b) a relativistic particle. 8 Calculate [Jx^2, Jy], [Jz^2, Jy] and [J2, Jy], and then show that
(c) \langle J, m | Jx2 | J, m \rangle = \langle J, m | Jy2 | J, m \rangle 8 Calculate the possible angles between \vecL and \vecS for a d-electron in one-electron
(d) atom. 8 The force constant of the bond in CO molecule is 1900 N m^{-1}. Calculate the
(e) energy of the lowest vibrational level. The reduced mass of CO molecule is 1.14 × 10-26 kg. Given h = 6.63 × 10-34 J s and 1 eV = 1.6 × 10-19 J. 8 Consider a particle of mass m and charge q moving under the influence of 2.
(a) an oven heated to a temperature of 400 K passes through a magnetic field of length 1 m and having a gradient of T/m perpendicular to the beam. Calculate the transverse deflection of an atom of the beam at a point where the beam leaves the field. The value of Bohr magneton μ_B is 9.27 × 10-24 A m2 and the Boltzmann constant k is 1.38 × 10-23 J/K. JBNV-B-PHYS/49 \overlinea