Question

A hydrogen-like ion has a nucleus of charge +Ze and a single electron outside this nucleus. The energy levels of these ions are -Z2 RH/n2 (where Z is the atomic number). Calculate the wavelength of the transition (nm) from n = 3 to n = 2 for He+, a hydrogen-like ion. What would be the perceived colour of this emission?

Answer 1

Are you sure about that formula you gave for the energy level? For some units that COULD be right. As it stands I don't that it is correct. I think it should be E = -hcRZ^2(1/n^2). Whatever formula you use, here is what you do. Calculate the E for n = 2 and E for n = 3. Z for He^+ = 2. Get the difference between E3 and E2(it should be positive) if you subtract correctly. Then delta E = hc/w where h is Planck's constant, c is speed of light in m/s and w is wavelength in m/s. You want the answer in nm. Convert remembering that 1 m = 10^9 nm. Post your work if you get stuck but check out that formula

Answer 2

1.64