an excited h like species when bombarded by photons of wavelength 54 nm gets excited to another excited state . in returning back to ground state a total of 6 different types of photons were emitted . out  of 6 photons three have wavelength less than 54 nm. determine
a. initial and final excited states
​b.ionization energy
​c.atomic number

Your case is given with insufficient data. But I can give the steps. 
First calculate the Wavelengths of the photons using1λ = 1λ1 + 1λ2 + 1λ3 + 1λ4 + 1λ5 + 1λ6For the first three its given < 54 nm, so the next three should be > 54 nmBut this value is not exact value. You should give some more details to calculatethe photons λ values. Second from the λ value set E should be calculated. E= hcλNext calculate the n1 and n2 values. E= RH z2 1n12 -1n22 Next ionisation energy = - EFor calculating atomic number either E value or λ value of the new species should be given. 

 

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