课程名称︰近代物理
课程性质︰电机系必选修
课程教师︰林清富
开课学院：电机资讯学院
开课系所︰电机系
考试日期（年月日）︰105/06/21
考试时限（分钟）：180分钟
试题 :
(注：上半张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)