To calculate the vibrational frequency of HCl in its ground state, we can use the following formula:v = 1/2 * k/ where v is the vibrational frequency, k is the force constant, and is the reduced mass of the HCl molecule.First, we need to find the reduced mass of the HCl molecule. The reduced mass is given by the formula: = m1 * m2 / m1 + m2 where m1 and m2 are the masses of the hydrogen and chlorine atoms, respectively. The atomic mass of hydrogen is approximately 1 amu, and the atomic mass of chlorine is approximately 35.5 amu. Converting these values to kilograms 1 amu = 1.66 x 10^-27 kg , we get:m1 = 1.66 x 10^-27 kgm2 = 35.5 * 1.66 x 10^-27 kgNow, we can calculate the reduced mass: = 1.66 x 10^-27 kg * 35.5 * 1.66 x 10^-27 kg / 1.66 x 10^-27 kg + 35.5 * 1.66 x 10^-27 kg 1.626 x 10^-27 kgNext, we need to find the force constant k for the HCl molecule. The force constant can be experimentally determined or found in literature. For HCl, the force constant is approximately 480 N/m.Now we can calculate the vibrational frequency v :v = 1/2 * 480 N/m / 1.626 x 10^-27 kg v 8.57 x 10^13 HzSo, the vibrational frequency of HCl in its ground state is approximately 8.57 x 10^13 Hz.