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(`a`) Since three radiations are emitted, therefore, the final excited state of the gas is `n=3`. <br> The initial state of the gas atoms is <br> `n=2` as all the wavelengths are smaller and the energy will be higher. <br> (`b`) `13.6Z^(2)[(1)/(2^(2))-(1)/(3^(2))]=68` <br> or `13.6Z^(2)[(5)/(36)]=68rArrZ=6` <br> (`c`) The minimum wavelength corresponds to the transition `n=3` to `n=1`. <br> `(1)/(lambda_(min))=RZ^(2)[(1)/(1^(2))-(1)/(3^(2))]` <br> or `lambda_(min)=(9)/(8RZ^(2))=(9)/(8(1.097xx10^(7))(6)^(2))=28.5Å` <br> (`d`) The ionization energy of the gas atoms is <br> `E=13.6Z^(2)=(13.6)(6)^(2)=489.6eV` <br> `lambda=(1)/(RZ^(2))=(1)/((1.097xx10^(7))(6)^(2))=25.32Å` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FIT_JEE_PHY_GMP_MOD4_C16_S01_015_S01.png" width="80%">