The force constant for the ³⁵ Cl₂ molecule is 323 N m⁻¹. Calculate the vibrational zero point energy of this molecule. If this amount of energy were converted to translational energy, how fast would the molecule be moving? Compare this speed to the root mean square speed from the kinetic gas theory, |v|ᵣ m s=√3 k_B T / m for T=300 . K.
a) 2.01 × 10⁻²¹ J; 63.4 m/s; 383 m/s
b) 4.02 × 10⁻²¹ J; 126.8 m/s; 383 m/s
c) 6.03 × 10⁻²¹ J; 190.2 m/s; 383 m/s
d) 8.04 × 10⁻²¹ J; 253.6 m/s; 383 m/s