Light/Frequency?

Question

Please help.

1. Find the energy required to ionize a ground state hydrogen atom. That is, what is the energy required to make the transition from n = 1 to n = inifinite.

I'm assuming use E = -R_h * Z^2 ( 1/n^2 final - 1/n^2 initial )
where n final is 0 (because infinite makes it equal to 0) and n initial is 1 and z = 1???

2. Calculate the frequency of light emitted when the electron in an He^+ ion relaxes from the third energy level to the first energy level.

I don't get this, Am i suppose to use the equation above but i need to change n final to 1 and n initial to 2 while changing z to 2 since 2 is He^+ atomic number and solve?

3. If an electron in a hydrogen atom relaxes to the second energy level, emitting a photon of wavelength 410.2 nm, what higher energy level did it start at?

I use e = hv, c = lambda * v (V = wavelength)

find the energy and plug into Rydberg's equation and solve right?

Thx =)

Answer 1

1. You are right that you need to use:
E = -R_h * Z^2 ( 1/n^2 final - 1/n^2 initial )
where R_h = 13.6eV or = 2.179×10^-18 J
BUT n final is NOT 0. n => inifinite means 1/n => 0 thus the whole equation becomes:
E = R_h * Z^2 /n^2 initial

2. You are supposed to use the same equation above but you need to change n final to 1 and n initial to 3 while changing z to 2 since 2 is He^+ atomic number and solve E.

3. You are right. Here n final = 2 and you are asked to find n initial (> 2)