I dont understand this. Help much appreciated. An electron is trapped along the

Question

I dont understand this. Help much appreciated.

An electron is trapped along the length of a molecule chain that is 2.0 nm long. This system is well modeled as an electron trapped in a one-dimensional box. The electron makes a transition from the n = 2 to the n = 3 state in this quantum system. Sketch the electron's de Broglie standing wave pattern in each of these states: Calculate the wavelength of the electron standing wave in each of these cases. n = 2: lambda = 2 nm n = 3: lambda = 2/3 middot 2 nm = 1.3 nm.

Explanation / Answer

by the definition of wavelengtth ,the distance between two successive crests or troughs

for n = 2

in figure only one wavelength is possibel

wavelength is lamda = 2 nm = 2*10^-9 m

for n = 3

here 1.5 wavelengths are possible

half of the wave length is lamda/2 = 2 nm/3 = 0.667 nm

then wavelength is 2*0.667 = 1.334 nm

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