Calculate the energy required to excited one litre of hydrogen gas at `1` atm and `298 K` to the excited state of atomic hydrogen. The energy for the disociation of H-H bond is `436 kJ mol^(-1)`. Also calculate the minimum frequency of photon to break this bond.

Options

A. `98.19 Hz`
B. `10.93xx10^(14) Hz`
C. `10^(15) Hz`
D. `6.22xx10^(14) Hz`

Answer

B

Explanation

Mole of `H_(2)` present in one litre `=(PV)/(RT)=(1xx1)/(0.0821xx298)=0.0409`
Thus, energy needed to break H-H bonds in `0.0409` mole `H_(2)=0.0409xx436=17.83 kJ`.
Also energy needed to excite one H atom from `1st` to `2nd` energy level
`=13.6(1-1/4)eV=10.2 eV=10.2xx1.6xx10^(-19) J`
`:.` Energy needed to excite `0.0409xx2xx6.02xx10^(23)` atoms of H
`=10.2xx1.6xx10^(-19)xx0.0409xx2xx6.02xx10^(23) J =80.36 kJ`
Thus, total energy needed `=17.83+80.36=98.19 kJ`
Energy required to break (H-H) bond `=(436xx10^(3))/(6.023xx10^(23))` joule
`E=hv " " :. (436xx10^(3))/(6.023xx10^(23))=6.625xx10^(-34) v`
`v=10.93xx10^(14) sec^(-1)` or Hz.