Ch26_1
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1) An electron is confined to a one dimensional box of x10
-11
m
. Estimate the minimal kinetic energy in
eV
using the uncertainty relation (
sheet 5,8
). (Set the uncartainty in the electron momentum to its full momentum). Indicate with a positive (negative) sign whether the electron kinetic energy can (cannot) be zero in the box.
2) A nucleus is in an excited state. The uncertainty in the lifetime of this state is x10
-12
s
. What is the minimal uncertainty in the energy of this state in
eV
(
sheet 5
) ? Indicate with a positive (negative) sign whether the uncertainty you calculated is (not) an experimental limitation.
3) A particle is confined in a one dimensional potential well of infinite height and width of x10
-14
m
. What is the maximum allowed wavelength of the particle wave in this well (
sheet 16
) in
nm
? Indicate with a positive (negative) sign whether this wave belongs to the highest (lowest) energy state.
4) A proton (mass = 1.67x10
-27
kg
) is confined in a one dimensional potential well of infinite height and width of x10
-14
m
. Calculate the kinetic energy of the proton in the state with quantum number in
MeV
(
sheet 16'
). Indicate with a positive (negative) sign whether all allowed energies in the well can (cannot) be related to each other by the ratio of integer numbers.
5) The wavefunction of a particle in a one dimensional potential well of finite depth contains halfwaves inside the well. What is the quantum number
n
(
sheet 16,25
) ?
6) The wavefunction of an atomic electron is
Y
(x)=
Y
0
e
-
a
x
,where x is the distance from the edge of the potential well binding the electron to the atom,
Y
0
=
Y
(x=0) and the coefficient
a
=x10
8
m
-1
. What is the ratio of the probability for the electron to be at the distance x10
-9
m
over the probability to be at x=0, at the edge of the potential well (
sheet 14,25
) ? Indicate with a positive (negative) sign whether the electron is (not) allowed to be outside the potential well in Classical Physics.
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