


1. 
a) 
Give a brief description of Rutherford’s alpha particle
scattering experiment. 

b) 
State the main conclusions of the experiment. 

c) 
An alpha particle of mass 6.68×10^{27}kg,
is moving straight towards a gold nucleus (atomic number, 79) at a
speed of 0.01c (0.01 times the speed of light). 


Calculate the minimum distance between the two particles (the
distance of closest approach). 



2. 

Bohr developed a model of the hydrogen atom. 

a) 
i) What particles enter into this model? 


ii) Describe the motion he assumed for each of the
particles. 


iii) What forms of energy did he include when calculating the
total energy of the atom? 


iv) What does it mean to describe a physical quantity as being
quantized? 


v) Which quantity did Bohr consider to be quantized when
developing his model? 

b) 
Use Bohr’s theory to explain why hydrogen emits a line
spectrum rather than a continuous spectrum. 



3. 

In a simplified version of Millikan’s oil drop experiment, a
drop of radius 1.75×10^{3}mm,
is between two parallel metal plates separated by distance d =
9mm. 











When the voltage across the plates, V =
2kV, the drop remains stationary. 


The density of the oil is 800kgm^{3}. 


Use this information to estimate the number of singly
ionized atoms in the drop. 



4. 

The diagram below represents the energy levels in a hydrogen
atom. 










a) 
Convert the energies into Joules. 

b) 
Calculate the wavelength of the radiation given out by each of
the three transitions shown on the diagram. 


In each case state whether the quantum of radiation is in the
u.v., the visible or the i.r. part of the spectrum. 

c) 
Calculate the wavelength of the radiation needed to ionize a
hydrogen atom which is in its ground state. 

d) 
Calculate the energy of an electron in level n = 5. 


Answer in electronvolts. 



5. 
a) 
Discuss briefly deBroglie’s hypothesis and mention one
experiment which gives evidence to support it. 

b) 
Calculate the wavelength of the “deBroglie wave” associated with 


i) a 1kg mass moving
at 50ms^{1} 


ii) an electron which has been accelerated by a p.d. of 500V 


iii) an electron in the lowest energy Bohr orbit, given that the
radius of the lowest energy orbit according to the Bohr theory is 5.3×10^{11}m. 



6. 

The diagram below shows a typical xray spectrum. 










a) 
Explain the characteristic (or line) part of an xray spectrum. 

b) 
Derive a formula to calculate the minimum wavelength of xrays
in the continuous part of an xray spectrum. 


Use your formula to calculate the highest frequency of xrays
given by a tube which uses a high voltage supply of 25kV. 