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Answer:
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