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1. A muon has the same charge as an electron, but its mass is 2105.7MeV / ,c  while the 
electron’s mass is just 20.511MeV / .c  We wish to calculate the ground state energy of a 
muonic atom (one proton and one muon in orbit).
To do so, we apply the formula for the ground state energy of a hydrogen atom with em  
replaced by .m  Thus we have
 
 
 
2 4
1 2
2
2
2
2
2
2
2
1
2
2
1 1
105.7 MeV
2 137.036
2814eV.
m k e
E
ke
m c
c
m c




 
 
   
 
 
 
   
 
 

2. The longest wavelength in the Lyman series  1fn   of the emission spectra of the 
Hydrogen atom is the wavelength of the light emitted by an electron making a transition 
from which excited state to the ground state?)
The longest wavelength transition comes from the lowest energy transition, since we 
have / .E hf hc    This transition comes from the first excited state  2 .in   

3. To ionize a hydrogen atom the electron has to be removed. If the hydrogen atom is in its 
ground state, the atom has to absorb light with what minimum frequency, minf ?
We have 1 min ,E hf  where 1 13.6eVE   is the ground state energy of the hydrogen 
atom. Thus we have
 
1
min
1
9
8 1
15 1
13.6eV 10 nm
3.00 10 ms
1240eV nm m
3.29 10 s .

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