A neutron is confined such that is has a nearly infinite energy outside a 0.100

Question

A neutron is confined such that is has a nearly infinite energy outside a 0.100 nm wide region of space but zero potential energy within that 1/10 of a nanometer (0.100 nm) 1-D space. What wavelength of electromagnetic radiation absorbed by the neutron in that system could result in a transition from the n=1 to the n=3 quantum level? Wavelength (show units) = What is the energy in Joules for the transition of an Avogadro's number of neutrons in this system to undergo the transition from n=1 to n=3? Energy in Joules = To what wavenumber in cm 1 does this transition from n=1 to n=3 correspond? Transition in cm^-1 =

Explanation / Answer

The neutron is confined in a 1D-box with 0.1nm length and is considered to be in a 1-D box

E = n 2 h/ 8meL2 = (6.626x10^-34 Js)2 / (8)x(1.674x10^-24Kg)x(1.0x10^-10 m)2 = 3.278 x 10 ^-24 j

(b) E3 - E1 = (9 -1) h/ 8meL2= 8x(3.278 x 10 ^-24) = 48.16x10^-18 J = 2.622 x 10^-23 J;

(a) E= hc/(wavelength)

wavelength=(6.626 x 10^-34) x 3x10^8 / 2.62 x 10^ -23 J = 7.587 x 10 ^-3 m

(c) wavenumber = 1/ 7.587 x 10 ^-3 x 100 = 1.318 cm-1

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