課程名稱︰近代物理
課程性質︰電機系複選必修
課程教師︰林清富
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰2017/11/23
考試時限（分鐘）：180
試題 :
Mid-term
(The following constants may be needed for solving the problems:
c = 3*10^10 cm/s, e = 1.6*10^(-19) C, h = 6.63*10^-34 J-s,
1 eV = 1.6*10^-19 J, 1 nm = 10^-9 m, 1 pm = 10^-12 m,
Mass energies: electron 0.511 MeV, proton 938 MeV, neutron 940 MeV.)
1. John is in a space shuttle that is moving toward the earth at a speed
of 0.5c. As he approaches the earth, he sends a signal at a rate of
1*10^9 pulses/second to Mary standing on the earth. What is the rate
that Mary receives this signal?(10 points)
2. Some particle has a lifetime of 1us at rest. If this particle has a
speed of 0.98c when it is created at some interaction, how far can
this particle go before it disappears?(10 points)
3. Please find the speed of electron when its kinetic energy calculated
from classical physics differs from the calculation from relativity
for 5%?(10 points)
4. A green light beam of 100 mW at the wavelength of 532 nm is incident
on a Si solar cell. If the light is completely absorbed by the solar
cell and 90% is converted to current. How much is the current?
(10points)
5. Some light at wavelength of 500 nm is generated from the surface of
the earth and escapes to the outer space. This light will experience
gravitational red shift. Please find the wavelength of this light
measured at the outer space.(10 points)(Hint: mass of earth =
5.972 * 10^24 kg, radius of earth = 6371km, gravitational constants
= 6.67*10^-11)
6. Please find the phase and group velocities of the de Broglie waves
of an electrons at the speed of 0.7c.(10 points)
7. The lowest energy possible for a particle trapped in a box with
infinite potential barrier is 0.5 eV. If the particle transits from
the first excited state to the ground state and emits a photon.
Please find the wavelength of the emitted photon.(10 points)
8. A beam of 12.6-eV electrons is used to bombard gaseous hydrogen.
What is the shortest wavelength of light can be emitted by the
hydrogen?(10 points)(Hint: the Rydberg constants is 1.097 * 10^7 m^-1)
9. A particle is in a cubic box with infinitely hard walls. The edge of
the cubic has a length of L. How many different wave functions are with
the energy lower than 10h^2/8mL^2, where h is the Planck constant, m is
the mass of the particle?(10 points)
10.Please find the expectation values <x> and <x^3> for the state with n =
2 of a harmonic oscillator.(10 points)