Question

a gas in a container is at a constant temperature t. the molecules have two vibrational energy states, the higher of which has energy 0.88kbt. there are 3000 molecules in this higher energy state and approximately 5500 in the lower state. what is the energy of the molecules in the lower state?

Answer 1

To find the energy of molecules in the lower state, we can use the concept of average kinetic energy. By setting up an equation using the given information, we can solve for the energy of the molecules in the lower state.

Step-by-step explanation:

The energy of the molecules in the lower state can be determined using the concept of average kinetic energy. In an ideal gas, the average kinetic energy per molecule is given by the equation K = (3/2)kBT, where K is the kinetic energy, kB is the Boltzmann constant, and T is the temperature of the gas in Kelvin. Since the total number of molecules in the higher energy state is 3000 and in the lower state is approximately 5500, the total energy of the higher energy state can be calculated by multiplying the number of molecules by the energy per molecule. Using the given value of 0.88kBT for the higher energy state, we can set up an equation to find the energy of the molecules in the lower state:

3000(0.88kBT) + 5500(E) = Total energy of the higher state

Substituting the equation for average kinetic energy and solving for E, we get:

5500(E) = Total energy of the higher state - 3000(0.88kBT)

Now, we can substitute the given temperature value of t Kelvin into the equation to obtain the energy of the molecules in the lower state.