Final answer:
To find the quantum number for the energy level at 3/2kT at 25 degrees Celsius, we need to equate the energy to 3/2kT and solve for n.
Step-by-step explanation:
The energy levels in a one-dimensional box for a helium atom can be calculated using the formula:
E = (n2 h2)/(8 mL2)
where E is the energy, n is the quantum number, h is Planck's constant, m is the mass of the helium atom, and L is the length of the box. To find the quantum number for the energy level at 3/2kT at 25 degrees Celsius, we need to equate the energy to 3/2kT and solve for n.
Using the given values, we can substitute k as Boltzmann's constant and T as the temperature in Kelvin.
Once we solve for n, we will find the quantum number of the energy level.