[試題] 104-2 林清富 近代物理 期末考
課程名稱︰近代物理
課程性質︰電機系必選修
課程教師︰林清富
開課學院：電機資訊學院
開課系所︰電機系
考試日期（年月日）︰105/06/21
考試時限（分鐘）：180分鐘
試題 :
(註：上半張考卷有附一些公式及constant的值)
1. A one-dimensional box with infinite potential barrier at the
boundaries is extending from x=0 to x=L. Please find the
probability of an electron trapped in this box to be found
between 0.4 L and 0.6 L. (10)
2. Please calculate the tunneling probably of an electron that
has an energy of 1.5 eV and is incident on a barrier 5.0 eV
high and 1 nm wide. (10)
3. Please find the expectation values of <x> for the ground state
of a harmonic oscillator. (5)
4. Please calculate the ratio of probability for an electron in the
ground state of a hydrogen atom to be found at the radius of a_0
and 2 a_0, where a_0 is the Bohr radius. (10)
5. A hydrogen atom is in the 4p state. To what state or states can it
go by radiating a photon in an allowed transition? Please explain
your answer. (10)
6. Please list the possible quantum numbers n, l, j, and m_j for the
3^2 P_1/2 state. (5)
7. Please calculate the wavelength of K_alpha x-ray emitted from an
element that has an atomic number of 27. (10)
8. Assume a diatomic molecule formed from the same element behaves
like a harmonic oscillator with a force constant of 900 N/m.
Please find the energy (in eV) of its ground and first excited
vibrational states. (10)
9. The Fermi energy of metal copper is 7.04 eV. Please evaluate the
percentage of the free electrons of copper in the excited states
at room temperature. (10)
10. Please describe the difference among metal, insulator, and
semiconductor from the view point of bandgap. (10)
11. When silicon is doped with Boron, will it become an n-type or
p-type semiconductor and how does the Fermi energy differ from
intrinsic Si? (10)
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