Question

a) Calculate the radius of the third orbit of Li2+ ion. Also calculate the energy of the electron in the second orbit of Li2+ ion.
Hint: Use equations derived for hydrogen atom in Unit 1.

b) Calculate (i) Rydberg constant for Be3+ ion and (ii) fourth ionization energy of beryllium in J atom-1 and kJ mol-1 units.

Answer 1

Answer on Question # 44187, Physics, Nuclear Physics

Task:

a) Calculate the radius of the third orbit of Li2+ ion. Also calculate the energy of the electron in the second orbit of Li2+ ion.

Solution:

the radius of the third orbit of Li2+ ion:

$$\begin{array}{l} r _ {n} = \frac {n ^ {2} h ^ {2}}{m _ {e} Z e ^ {2}} \Rightarrow r _ {3} = \frac {3 ^ {2} (1 . 0 5 4 \cdot 1 0 ^ {- 3 4}) ^ {2}}{9 . 1 \cdot 1 0 ^ {- 2 1} \cdot 3 (1 . 6 \cdot 1 0 ^ {- 1 9}) ^ {2}} = 0. 1 4 3 \cdot 1 0 ^ {- 9} = 1. 4 3 \cdot 1 0 ^ {- 1 0} m \\ E = \frac {m _ {e} Z ^ {2} e ^ {4}}{2 n ^ {2} h ^ {2}} = \frac {9 . 1 \cdot 1 0 ^ {- 2 1} \cdot 3 ^ {2} (1 . 6 \cdot 1 0 ^ {- 1 9}) ^ {4}}{2 \cdot 2 ^ {2} (1 . 0 5 4 \cdot 1 0 ^ {- 3 4}) ^ {2}} = 6 0. 3 9 \cdot 1 0 ^ {- 2 9} J \\ \end{array}$$

b) Calculate (i) Rydberg constant for Be3+ ion and (ii) fourth ionization energy of beryllium in J atom-1 and kJ mol-1 units.

Solution:

$$R = \frac {2 \pi^ {2} m _ {e} Z ^ {2} e ^ {4}}{h ^ {3} c} = \frac {2 \cdot 3 . 1 4 \cdot 3 . 1 4 \cdot 9 . 1 \cdot 1 0 ^ {- 2 1} \cdot 4 ^ {2} (1 . 6 \cdot 1 0 ^ {- 1 9}) ^ {4}}{(1 . 0 5 4 \cdot 1 0 ^ {- 3 4}) ^ {3} \cdot 3 \cdot 1 0 ^ {8}} = 5. 3 5 m ^ {- 1}$$

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