## Tuesday, 10 May 2011

### Problem set: Atomic world

Unit 1: Semi-classical view of atomic models.
1)       a) Describe the plum model.
b) Give one limitations of plum model, with mathematical interpretation.
2)       Concerning alpha particle scattering experiment:
a)       Explain why alpha particle and lead shield is used.
b)       With the light of plum model, explain why electron of the gold atom has negligible effect on the alpha particle.
c)       Account the possibility of 180º turnaround of alpha particle.
3)       An alpha particle of speed 3*107 ms-1 collide with a silver nucleus linearly and rebounds. Calculate the closest distance between the alpha particle and the silver nucleus.
4)       a) Give one limitation of Rutherford's atomic model.
b) Positron is produced under gamma radiation on a certain particles.
i) It vanishes under collision with electron. Calculate the energy released in eV.
ii) State one method to separate electron and positron.
iii) Give a name of this kind of experiment.
Unit 2: Photoelectric effect
1)       A zinc plate is connected to a gold leaf electroscope. State the observation if:
a)       The zinc plate is negatively charged and being shone by a sodium lamp.
b)       The zinc plate is positively charged and being shone by a UV lamp.
c)       The zinc plate is negatively charged and being shone by a UV lamp.
2)       Sketch a Ip-V graph. State the physical meaning of -Vs instead of Vs.
3)       Find the speed of electron which is accelerated from still by a p.d. of 10V.
4)       Given that the photoelectric current detected is zero. State one deduction.
5)       Concerning the properties of photoelectric effect:
a)       State two properties of photoelectric effect which wave theory can't explain with explanation.
b)       Explain the above two properties by quantum theory.
c)       Explain the term intensity in terms of wave and quantum theory respectively.
6)       A beam of monochromatic light has frequency 10-9m.
a)       The source of the light has power rating 100W. Calculate the number of photons emitted per second.
b)       The light is directed on a piece of metal with working function 3eV. Find the stopping potential.
Unit 3: Bohr's atomic model.
1)       Define continuous spectrum and absorption spectrum. Hence explain the formation of absorption spectrum.
2)       State two classical formulas that being considered as postulates of Bohr's model.
3)       Considering the energy level of the hydrogen atom:
a)       Show that U = EPE/2, hence show that U = e2/8πε0r.
b)       Considering the centripetal force of orbital motion of electron, derive the formula of energy and orbital radius of electron at a certain energy level.
c)       State the radius, energy and physical meaning of E. Hence state the physical meaning of "electrons with energy level beyond E".
4)       Find the requiring energy for:
a)       Exciting energy of hydrogen atom from ground to 3th excited state.
b)       Ionization energy of hydrogen atom from 6th excited state.
5)       Find the wavelength of EM waves emitted for a transition in Balmer series from n=6.
6)       The electron of hydrogen atom is at the ground state. Find the transition (if happened):
a)       A photon with wavelength 122 nm collides with the electron.
b)       A photon with wavelength 144 nm collides with the electron.
c)       A photon with wavelength 0.34 nm collides with the electron.
7)       The first four energy levels of a heavy metal atom is -2.5MeV, -1.5MeV, -790keV and -230keV. The electron is now at the first excited state.
a)       Find the frequency of photon required to transit the electron to n=3.
b)       Find the wavelength of photon emitted to transit the electron to n=1.
c)       It's given that photon of frequency f1 transits the electron to n=a and another photon of frequency f2 transits the electron again to n=b. Show that a photon of frequency f1+f2 directly transit the electron to n=b.
d)       A student plans to use an accelerated free electron to provide energy to the electron in the atom to make a transition. Comment whether it is practical or not.
Unit 4: Wave-particle duality
1)       State two evidences for wave and particle property of photon/EM wave respectively.
2)       Determine whether the following phenomena refer to wave or particle property.
a)       Refer to relativity theory, all observers observes the speed of light is c.
b)       Photoelectric effect
c)       Individual counts in GM counter. (Instruments measuring radioactivity)
3)       A car of mass 1200kg drives at the speed of 1ms-1. Find its De Broglie wavelength.
Unit 5: Nanotechnology
1)       Define size of nanoscale. Hence express the size of atom in terms of nanoscale.
2)       Give three examples of allotropes of carbon atom.
3)       a) Explain why carbon nanotubes can have a higher tensile strength than bulky metals.
b) Explain with diagram with carbon nanotubes can have a higher thermal conductivity.
c) Define ferromagnetic and paramagnetic materials and give one example for each material.
d) A cube is cut into 27 (33) smaller cubes of equal size. Find the surface area to volume ratio. Hence deduce that the above ratio can be infinitely big.
4)       Define lotus effect and give one application.
5)       Assume a lens do not have any optical abbreviations. Explain whether his lens do not give error.
6)       Two point objects are observed by a microscope under light of wavelength 600nm, the objective lens of the microscope has an aperture of size 5mm and focal length of 19mm. Find the resolving power of the microscope.
7)       Give a reason that the object in TEM must be thin enough.
8)       Find the p.d. acquired to accelerate electron in TEM so that it can have wavelength 0.02nm. Hence find the resolving power of the TEM.
9)       Given the typical distance between specimen and probe of STM. Compare the tunnelling current if the distance is widening by 10 times.
10)   a) STM don't scan the "colour" of the object as we observed. Explain.
b) Waves on the object are observed in STM image. Explain.
11)   Give one precaution when handling nanomaterials.
Mixing problems:
1)       Consider the nucleus of helium (4He) as a point mass. Calculate the energy level of a Helium atom.
2)       Assume En=E1/n2 and Bohr's model is correct for all atoms. Explain photoelectric effect by Bohr's model.
3)       An electron beam is accelerated by 50kV and passed a double slit and project on a fluorescent screen.
a)       The slit separation is 100nm, find the angle for the first three maxima.
b)       Identify wave and particle behavior in this experiment.
c)       Describe the result when only one electron passes through the double slit by probability wave.

Disclaimer:
1) My friend and me created this.
2) We are not familiar with problems concerning Rayleigh criteria, so Ch.5Q6 is just a typical modified question.
3) This is uploaded in the note page (with some fixed stuff for the note set), I just checked the 1980-1989 AL past paper structured questions for these three questions. I'm sorry that there's no past questions for Bohr's model included. Neither for duality too (though I think it's included in the HKU Higher level exam.)

Note:
1) We neglect all non-classical effect here, except the quantum theory introduced.
2) If the problem is contradictory to modern theory, you're welcome to comment here/tell me what's wrong.