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find the energy needed to remove an electron completely from a hydrogen atom and the energy needed to remove one mol of electrons from one mol of hydrogen atoms

Z= 1 nhigh= infinity nlow=1

E = 2.178*10^-18 J

one mole of electrons = 2.178*10^-18 * 6.022*10^23 = 1.312*10^6 J/mol

Are these right??

And use the above formula to find the value of Z for an ion whose 2 to 1 transition is associated with a wavelength of 13.4nm.

lamba of 2 to 1= hc/(2.178*10^-18 * Z^2/nhigh^2 - nlow^2)

z=sqrt(hc(nhigh^2-nlow^2)/(13.4*10^-9)(2.178*10^-18))

Z= 4.5

or 5

Is this right??

Thank you guys so much for your help.

Stephen