PHYS 2004 Lecture Notes - Lecture 27: Standing Wave, Bohr Model

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1 Dec 2017

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The particle in the box forms a standing wave, and its wavelength is the de broglie wavelength h/mv, so (cid:449)e (cid:272)an sol(cid:448)e for the parti(cid:272)le"s speed: This particle must have one of the specific speeds vn. The parti(cid:272)le"s energy, (cid:449)hi(cid:272)h is purely kinetic energy, is. The possi(cid:271)le (cid:448)alues of the parti(cid:272)le"s energy are (cid:272)alled energy levels, and the integer n that characterizes the energy levels is called the quantum number. The electrons in an atom can exist in only certain allowed orbits.

Related Questions

1) We shine light onto a metal surface. We observe that someelectrons are emitted from the metal surface if the frequency ofthe light exceeds some critical frequency f0 = F/h, where F = thework function for this metal. What happens if the light's frequencyf is less than f0? ( Ignore reflections off the metalsurface.)

a) The electrons leave the metal but are attracted back toit.
b) The photons get absorbed by the electrons but the electrons stayinside the metal.
c) Whether or not any electrons leave the metal depends on theintensity of the light.

2) Now we shine light of a frequency f > f0 onto the metalsurface and in addition apply a voltage V between the metal and theelectrode. What happens if V is a tiny bit larger than (1/e) (hf -F )?

a) Some electrons barely make it to the other electrode.
b) All electrons turn around before reaching the otherelectrode.
c) No electrons escape the metal.

3) Consider a photon with a frequency of 1 GHz. What is the ratioof its wavelength ?? to the de Broglie wavelength ?e of an electronwith the same kinetic energy? (Note: It is standard to use thesubscript '?' to stand for photons.)

??/?e =
a) 2.01e-006
b) 1.21e-003
c) 1
d) 8.24e+002
e) 4.97e+005

4) The mass of the electron is 0.511 Mev/c2. A muon Âµ can beregarded as an electron with mass mÂµ = 105.7 MeV/c2.
Let the muon have kinetic energy E.
Define ?Âµ to be the de Broglie wavelength of the muon with energyE.
Define ?e to be the de Broglie wavelength of an electron with thesame energy E.
Calculate the ratio of wavelengths ?Âµ/?e.

?Âµ/?e =

a)0.005
b)0.070
c)1.
d)14.382
e)cannot be determined from the information given
5) Electrons diffract when passing through a small hole in ascreen. If we make the hole smaller, the angular spread in thediffracted electrons will

a) decrease.
b) stay the same.
c) increase.

PHYS 2004 Lecture Notes - Lecture 27: Standing Wave, Bohr Model

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