The electron in a hydrogen atom make a transtion `n_(1) rarr n_(2)` where `n_(1) and n_(2)` are the priocipal quantum number of the two states . Assume the Bohr model to be valid . The time period of the electron in the initial state is eight time that in the state . THe possible values of `n_(1) and n_(2)` are
A
`n_(1) = 4 , n_(2) = 2 `
B
`n_(1) = 8 , n_(2) = 2`
C
`n_(1) = 8 , n_(2) = 1 `
D
`n_(1) = 6 , n_(2) = 3`
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The correct Answer is:
A, D
The time period of the electron in a bohr is given by `T = (2 pi r )/(nu)` Since the for the bohr orbit , `m nu r = n (h//2 pi) ` , the time period because `T = (2 pi r)/(nh//(2 tau m r )) = ((4 pi ^(2) m)/(nh))` since the radius of the orbit r depends on n, we replace r bohr radius of a hydrogen atom is `r = n^(2) ((h^(2)epsilon _(0))/(tau me^(2))` Hence , T = ((4 pi ^(2) m)/(nh)) (( n^(2) h^(4) epsilon_(0)^(2))/(pi ^(2) m^(2) e^(4))) = n^(2) (( 4h^(3) epsilon_(0)^(2))/(me^(4)))` `for two orbit `T_(1))/(T_(2)) = (( n_(1))/(n_(2))) ^(2) ` it is given that `T_(1) //T_(2) = 8 ,` heanse `n_(1)//n_(2) = 2 `
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