Homework-14-solns

Homework-14-solns - Homework 14 Chapter 31 SOLUTIONS...

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Homework 14 – Chapter 31 – SOLUTIONS QUESTION 1 Find the energy of photon required to excite a hydrogen atom from n = 2 state to n = 5 state. (Express your answer in the unit of electron-volt). SOLUTION E = E 5 E 2 = 13.6 eV 5 2 13.6 eV 2 2  E = 2.86 eV QUESTION 2 Find (a) the radius of the n = 4 Bohr's orbit of a doubly ionized atom (Li 2+ , Z = 3), and (b) the energy (in unit of eV) needed to raise the electron from n = 4 state to n = 5 state. SOLUTIONS Note that the doubly ionized Li ++  atom has only one electron, so we can use the Bohr model of Hydrogen to find its energies and radii. But we will have to remember that the Lithium nucleus has  Z  = 3. So the Bohr formulas for Hydrogen get modified to: E n =− 13.6 eV Z 2 n 2 (see eqn 31-9) r n = 5.29 × 10 11 m n 2 Z (see eqn 31-7) (a)  r 4  =  (5.29 x 10 -11 ) (4 2 ) / 3 =  2.82 x 10 -10  m (b)  E = E 5 E 4 =− 13.6 eV Z 2 [ 1 5 2 1 4 2 ] =− 13.6 eV  3 2 [ 1 25 1 16 ] E  = 2.754 eV
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QUESTION 3 How many different values of  m 1  
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