A π -meson hydrogen atom is a bound state of negatively charged pion (denoted by π – , m π = 273 m e ) and a proton. Estimate the number of revolutions a π -meson makes (averagely) in the ground state of the atom before it decays (mean life of a π -meson 
10 –8 sec).
Text Solution
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Sol. In Bohr’s model of hydrogen atom, the radius of the n th orbit is given as
r n = 
, where k = 
Radius for n = 1 of π -meson atom (ground state) will be
r n = 
= 
= 1.93 × 10 –13 m
or r n = 
(in Å) = 1.93 × 10 –13 m
Velocity of nth orbit v = 
For n = 1, v = 
= 2.19 × 10 6 m/s
Time of one revolution
T = 
= 
= 5.5 × 10 –19 s
Probable number of revolutions before π -meson decay
= 
= 
= 2 × 10 10
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