A deuterium molecule (D₂) at 30°K is known to be in the state, 124): 263|1, 1) + 4 (7,3) + 17,1)] where , m) are eigenstates of the angular momentum operator. (a) If one were to measure L₂, what posible values one would get and what would be their associated probabilities? (b) Repeat (a) but for L². (c) What is the expectation value of the energy (E) of the molecule in this state, assuming purely rotational states. Take 4c = 30.4 cm−¹, where I=moment of inertia of D₂ and c=speed of light. Express your answer in eV.

A deuterium molecule (D₂) at 30°K is known to be in the state, 124): 263|1, 1) + 4 (7,3) + 17,1)] where , m) are eigenstates of the angular momentum operator. (a) If one were to measure L₂, what posible values one would get and what would be their associated probabilities? (b) Repeat (a) but for L². (c) What is the expectation value of the energy (E) of the molecule in this state, assuming purely rotational states. Take 4c = 30.4 cm−¹, where I=moment of inertia of D₂ and c=speed of light. Express your answer in eV.