Photons emitted by Hydrogen and helium atoms

[Elvis 123456789]

Homework Statement

An excited hydrogen atom can emit photons of various wavelengths.

a) What is the maximum wavelength of the Balmer series (in nm) (5pt)

b) What is the minimum wavelength of the Balmer series (in nm) (5pt)

c) Corresponding to part b), what is the kinetic energy of the recoil hydrogen atom, in the unit of eV? ( mH = 938MeV / c 2 )10pt)

d) Assume the helium atom (Z=2) has the mass that is 4 times of hydrogen, what should happen to your answer to part c), if the atom is changed from hydrogen to helium. Show you results in terms of KHe / KH = ? (10pt)

Homework Equations

1/λ = R (1/n_f² -1/n_i²)

R = 1.097*10⁷ m^-1

mv = E_photon/c ----> due to momentum conservation

KE = 0.5 * (mv)² * 1/m

The Attempt at a Solution

a.) max wavelength happens when energy level goes from n = 3 to n = 2

λ_max = 656 nm

b.) the min wavelength happens when the energy level goes from n = ∞ to n = 2

λ_min = 365 nm

c.) E_photon = h*c/λ_min = 3.41 eV
m_H = 938 MeV/c²

KE_H = 6.19 GeV

d.) I'm not sure how to do this part since the rydberg equation is meant to be used with hydrogen

 

[Simon Bridge]

You have a derivation for energy levels of general hydrogenic atoms which has Z in it.
The Rydberg formula is derived from this with Z=1.

 

[Elvis 123456789]

We never covered this in class but I found the equation with the included Z² term in it. But would I then use the same R value or is there some specific helium R?

 

[Simon Bridge]

You can answer that yourself by looking at the definition of "R".
Note: you almost certainly covered this in class.
Where did you find the equation with the R value in it?