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Imagine a atom made up of proton and a hypothetical particle of double the mass of electron but having the same charge as electrons. Apply the Bohr atokic model and consider all the possible transitions of this hypothetical particle to first excited level. The largest wavelength photon that will be emitted has wavelength (lamda) (given in terms of Rydberg constant R for the hydrogen atom) equals to:
1) 9/5R
2) 36/5R
3) 18/5R
4) 4/R
hi.
rydberg const. is directely proportional to the first power of m
so , rydberg const for the new atom , R' = 2R
largestwavelength will be emitted in this case when the transition occurs from 3rd excited state to first
1/λ = R' { 1/2^2 - 1/3^2 }
= 2R { 1/4 - 1/9 }
= 5R/18
λ = 18/5R (3)
In h-atom;
E(n)=-Rhc/(n*n)
Also, E(n) is proportional to m
m is mass of electron.
As m-->2m, E(n)=-2Rhc/(n*n)
for largest wavelength(x), 1/x=R((1/4)-(1/9))
x=18/5R
Hence (C)
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