In a mixture of `H- He^(+)` gas (`He+ `is singly ionized He atom), `H` atom and `He+` ions are excited to their respective first sxcited state subequendy `H` atoms transfer their total excilation energy to `He+` ions (by collsions) Assume that the bohr model of atom is exactly veld. The questum number `n` of the state fnally populand in `He^(+)` inos is -
A
`2`
B
`3`
C
`4`
D
`5`
Text Solution
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The correct Answer is:
C
For hydrogen like atom `E_(0) = (-13.6 Z^(2))/(n^(2))eV // atom ` `(for hydrogebn atom)/((Z= 1))` E_(1) = - 13.6 eV` `E_(2) = -3.4 eV` :.delta E = E_(2) - E_(1) = - 3.4 - (-13.6 ) = 10.2 eV` i.e. when hydrogen comes to ground state it will release `10.2 eV` of energy `(for He^(+)ion)/((Z = 2))` E_(1) = - 13.6 xx 4 eV = - 54.4 eV ` `E_(2) = -13.6eV` `E_(3) = - 6.04eV` `E_(4) = - 3.4 eV` Here `He^(+)` ion is in first excited state i. e. possessing energuy `= 13.6eV` . After receiving of `+ 10.2 eV` from excited hydrogen atom on collsion , the energy of electron will be `(-13.6 + 10.2) eV = -3.4 eV` This means that the electron will jump to `n = 4`
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