Using the Rydberg equation (delta E = RH(1/n2^2 - 1/n1^2) ), show that the energy of the transition from the lowest state (n1=1) to the highest energy state (n2=infinity) is given by delta E (kJ/mol) = -RH. Therefore, the magnitude of this constant is equal to the ionization energy of one mole of hydrogen atoms, in units of kJ/mol. How do I go about doing this?
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Evaluate the two terms in the parentheses (1/n2^2 - 1/n1^2) at the specified values.
(A) 1/n2^2
As n2 approaches infinity, 1/n2^2 approaches zero; therefore, at infinity we can consider this term to be equal to zero.
(B) 1/n1^2
For n1 = 1, n1^2 = 1, and therefore 1/n1^1 = 1
Substitute these values in the original equation and simplfy:
delta E = RH(1/n2^2 - 1/n1^2) = RH(0 - 1) = -RH
(A) 1/n2^2
As n2 approaches infinity, 1/n2^2 approaches zero; therefore, at infinity we can consider this term to be equal to zero.
(B) 1/n1^2
For n1 = 1, n1^2 = 1, and therefore 1/n1^1 = 1
Substitute these values in the original equation and simplfy:
delta E = RH(1/n2^2 - 1/n1^2) = RH(0 - 1) = -RH