- #1

Elvis 123456789

- 158

- 6

## 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

_{f}

^{2}-1/n

_{i}

^{2})

R = 1.097*10

^{7}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 nmb.) the min wavelength happens when the energy level goes from n = ∞ to n = 2

**λ**= 365 nm_{min}c.) E

_{photon}= h*c/λ

_{min}= 3.41 eV

m

_{H}= 938 MeV/c

^{2}

**KE**

_{H}= 6.19 GeVd.) I'm not sure how to do this part since the rydberg equation is meant to be used with hydrogen