Question

An electron confined to a one-dimensional box has energy levels given by the equation

En=n2h2/8mL2

where n is a quantum number with possible values of 1,2,3,…;m is the mass of the particle; and L is the length of the box.

a. Calculate the energies of the n=1,n=2, and n=3 levels for an electron in a box with a length of 170 pm .

b. Calculate the wavelength of light required to make a transition from n=1→n=2 and from n=2→n=3.

c.

In what region of the electromagnetic spectrum do these wavelengths lie?

radio |

microwave |

infrared |

visible light |

ultraviolet |

X-ray |

gamma ray |

Step 1

a. An electron confined to a one-dimensional box has energy levels given by the equation

Step 2

The energy of each level is calculated as,

Step 3

b. The wavelength required for tran...

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