Problems of the 7th International Physics Olympiad
1
(Warsaw, 1974)
Waldemar Gorzkowski
Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
2
Abstract
The article contains the competition problems given at the 7th International Physics
Olympiad (Warsaw, 1974) and their solutions.
Introduction
The 7
th
International Physics Olympiad (Warsaw, 1974) was the second one organized
in Poland. It took place after a oneyear organizational gap, as no country was able to
organize the competition in 1973.
The original English version of the problems of the 7
th
IPhO has not been preserved.
We would like to remind that the permanent Secretariat of the IPhOs was established only in
1983; previously the Olympic materials had been collected by individual people in their
private archives and, in general, are not complete. English texts of the problems and
simplified solutions are available in the book by R. Kunfalvi [1]. Unfortunately, they are
somewhat deformed as compared to the originals. Fortunately, we have very precise Polish
texts. Also the full solutions in Polish are available. This article is based on the books [2, 3]
and article [4].
The competition problems were prepared especially for the 7
th
IPhO by Andrzej
Szymacha (theoretical problems) and Jerzy Langer (experimental problem).
THEORETICAL PROBLEMS
Problem 1
A hydrogen atom in the ground state, moving with velocity
v
, collides with another
hydrogen atom in the ground state at rest. Using the Bohr model find the smallest velocity
0
v
of the atom below which the collision must be elastic.
At velocity
0
v
the collision may be inelastic and the colliding atoms may emit
electromagnetic radiation. Estimate the difference of frequencies of the radiation emitted in
the direction of the initial velocity of the hydrogen atom and in the opposite direction as a
fraction (expressed in percents) of their arithmetic mean value.
Data:
J
18
2.18
eV
6
.
13
2
18

2
4
⋅
=
=
=
me
E
i
; (ionization energy of hydrogen atom)
kg
10
67
.
1
27

⋅
=
H
m
; (mass of hydrogen atom)
1
This article has been sent for publication in
Physics Competitions
in September 2003
2
email: [email protected]
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(
m
 mass of electron;
e
 electric charge of electron;
 Planck constant; numerical
values of these quantities are not necessary.)
Solution
According to the Bohr model the energy levels of the hydrogen atom are given by the
formula:
2
n
E
E
i
n

=
,
where
n
= 1, 2, 3, … The ground state corresponds to
1
=
n
, while the lowest excited state
corresponds to
2
=
n
. Thus, the smallest energy necessary for excitation of the hydrogen atom
is:
i
i
E
E
E
E
E
4
3
4
1
1
2
)
1
(
=

=

=
∆
.
During an inelastic collision a part of kinetic energy of the colliding particles is
converted into their internal energy. The internal energy of the system of two hydrogen atoms
considered in the problem cannot be changed by less than
E
∆
. It means that if the kinetic
energy of the colliding atoms with respect to their center of mass is less than
E
∆
, then the
collision must be an elastic one. The value of
0
v
can be found by considering the critical case,
when the kinetic energy of the colliding atoms is equal to the smallest energy of excitation.
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 Physics, Atom, Energy, Fig., Hydrogen atom, Black Box, v0

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