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 αc n ) 2 . The allowed transition frequencies are f = E n − E m h = 4 m e ( αc ) 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 αc ) 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 π 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 π 2 2 mL 2 = (2 n + 1) ¯ h 2 π 2 2 mL 2 ∼ 2 n ¯ h 2 π 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 electron’s average momentum will be zero, but the uncertainty in its momentum is approximately equal to its momentum...
View
Full Document
 Fall '07
 Scholberg
 Physics, Electron, Kinetic Energy, Photon, Uncertainty Principle

Click to edit the document details