Chemistry

Problem

The single-electron ion

\text{He}^{+}

(atomic number

Z = 2

) is observed in a state whose orbital angular momentum is

3\hbar

. Use

a_0 = 0.529\times10^{-10}\,\text{m}

for the Bohr radius and

e = 1.60\times10^{-19}\,\text{C}

. a. (i) Identify the principal quantum number

n

of this state. b. (ii) Calculate the radius of the electron’s orbit in this state. c. (iii) Determine the orbital speed of the electron. d. (iv) Compute the total energy of the electron in this orbit.

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