Question

3rd time to post this question.

Found in the gas phase the Be⁺³ cation has an energy level formula analogous to that of the hydrogen atom, since both species have only one electron. The energy levels of the Be⁺³ ion are given by the equation

E_n = -21001/n² kJ/mol, where n = 1, 2, 3....

As n increases, the electron becomes farther from the nucleus. When n is infinite, the electron has been completely removed from the atom. What is E_infinity for Be³⁺ in kJ/mol?

So far wrong answers are as follows: 2.61x10^-32, 2.61x10^-14, E_infinity=R_h[1/n₁² - 1/n_^`iinfinity²] where R is rydberg constant which it does not let me enter, has to be a number and my canvas is not allowing any powers of ten or exponents.

Answer 1

rydber eq is wavenumber = Z^2 x 10973731.6 ( 1/n1^2 -1/n^2) where n1 = 1 , n2 = infinity

and Z = atomic number of Be = 4

hence wavenumber = ( 4^2 x 10973731.6) ( 1/1^2 -0) = 175579705.6

E = n x h x c x wavenumber    wher n = avagadro number

E = 6.023 x 10^23 x 6.625 x 10^-34 x 3x10^8 x 175579705.6

= 21018141 J /mol = 21018 KJ/mol ,

or elese we can actally use the energy level mention En = -21001/n^2 KJ/mol

where 1/n^2 = 0 hence En = -21001 KJ/mol

Better to use value of 21001 KJ/mol since they mentioned it