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For a helium atom in a one-dimensional box calculate the value of the quantum number of the energy level for which the energy is equal to 3/2kT at 25 degrees C

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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.

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