An electron is trapped in a one-dimensional infinite well of width 340 pm and is in its ground state. what are the (a) longest, (b) second longest, and (c) third longest wavelengths of light that can excite the electron from the ground state via a single photon absorption?

(a) 1.2703×10⁻⁷ m

(b) 4.7636×10⁻⁸ m

(c) 2.5406×10⁻⁸ m

Explanation:

Given:

Width of the infinite well, L = 340 pm = 340×10⁻¹² m.

The formula for energy of the electron in nth state is:

The expression for the difference in energy between the levels having quantum numbers n(initial) to n(final) is:

According to Planks theory:

E = hv

where, v is the frequency

Also,

Frequency×Wavelength = Speed of light

So,

Also,  using energy from above formula as:

For longest wavelength ni = 1 and nf = 2

m= mass of the electron = 9.1 ×10⁻³¹kg

c = 3×10⁸m/s

h = 6.625×10⁻³⁴J.sec

Longest wavelength = 1.2703×10⁻⁷ m

For second longest wavelength ni = 1 and nf = 3

Second longest wavelength = 4.7636×10⁻⁸ m

For third longest wavelength ni = 1 and nf = 4

Third longest wavelength = 2.5406×10⁻⁸ m

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