This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Duke University Department of Physics Physics 143 Fall Term 2007 PRACTICE QUIZ 2 SOLUTIONS Problem 1: Consider a helium atom which has had one of its electrons stripped. What formula will describe the frequencies of the spectral lines for this He + ion? Find an expression for the energy required to remove the remaining electron in its ground state. Solution: The nucleus has Z = 2. The allowed energy levels are therefore E n = 1 2 m e ( 2 c n ) 2 . The allowed transition frequencies are f = E n E m h = 4 m e ( c ) 2 2 h ( 1 n 2 1 n 2 ) The energy required to remove the remaining electron (the ionization en- ergy) corresponds to a final state of n , and n = 1, so 1 2 m e (2 c ) 2 . Problem 2: A 1.00 g marble is constrained to roll inside a tube of length L = 1 . 00 cm. Modeling this as a 1D infinite square well, find the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. Calculate the energy required to promote the marble to the next available energy state. Solution: E n = n 2 h 2 2 2 mL 2 Plugging in and solving for n gives n = 4 . 5 10 28 . The energy required to get to the next state is E n +1 E n = (( n + 1) 2 n 2 ) h 2 2 2 mL 2 = (2 n + 1) h 2 2 2 mL 2 2 n h 2 2 2 mL 2 and plugging in, get this to be 5 10 32 J. Problem 3: An electron of momentum p and mass m e is at distance r in a circular orbit around a stationary proton. The system has kinetic energy K = p 2 / 2 m e and a potential energy U = ke 2 /r . The average position of the electron is at the proton but the uncertainty of its position is approximately equal to the radius r of its orbit. The electrons average momentum will be zero, but the uncertainty in its momentum is approximately equal to its momentum...
View Full Document
- Fall '07