When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid. These dissolved electrons absorb light with a wavelength near 800. nm. Suppose we treat the positive ions surrounding an electron crudely as defining a three-dimensional cubic box of edge , and we assume that the absorbed light excites the electron from its ground state to the first excited state. Calculate the edge length in this simple model.

The edge of the length is

Explanation:

From the given information:

The associated energy for a particle in three - dimensional box can be expressed as:

here;

h = planck's constant =

= the quantum no in a specified direction

m = mass (of particle)

L = length of the box

At the ground state

The energy at the ground state can be calculated by using the formula:

At first excited energy level, one of the quantum values will be 2 and the others will be 1.

Thus, the first excited energy will be: 2,1,1

∴

The transition energy needed to move from the ground to the excited state is:

----- (1)

Recall that:

the  wavelength identified with the electronic transition is: 800 nm

800 nm = 8.0  × 10⁻⁷ m

However, the energy-related with the electronic transition is:

Replacing the value of in (1); then:

Making the edge length L the subject of the formula; we have:

Thus, the edge of the length is

d.) the average kinetic energy of the gas particles is greater in container b because its particles move faster.

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