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Chapter 3: Problem 18

For each of the questions, four choices have been provided. Select the correct alternative. What is the maximum number of electrons, present in an orbit whose angular momentum is \(\frac{2 \mathrm{~h}}{\pi}\) ? (a) 18 (b) 2 (c) 32 (d) 8

Short Answer

Expert verified
Answer: The maximum number of electrons in the orbit is 8.

Step by step solution

01

Recall Bohr's Quantization Rule

According to Bohr's quantization rule for angular momentum, the angular momentum of an electron in an orbit \((L)\) is given by: \(L = mvr = \frac {nh}{2\pi}\) Where \(m\) is the mass of the electron, \(v\) is its velocity, \(r\) is the radius of the orbit, \(n\) is the principal quantum number, and \(h\) is the Planck's constant.
02

Find the principal quantum number (n)

In this exercise, we are given the angular momentum of the orbit as \(\frac{2h}{\pi}\). We will use Bohr's quantization rule to find the principal quantum number by equating the given angular momentum with the formula: \(\frac{2h}{\pi} = \frac {nh}{2\pi}\) Dividing both sides by \(h\) and multiplying by \(2\pi\), we obtain: \(2 = n\) So, the principal quantum number (\(n\)) for this orbit is 2.
03

Determine the maximum number of electrons

The maximum number of electrons in an orbit can be determined using the formula: \(max~electrons = 2n^2\) Substituting the value of \(n\) we found in step 2, we get: \(max~electrons = 2(2^2) = 2(4) = 8\) The maximum number of electrons in the orbit is 8, which corresponds with choice (d) in the exercise.

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Most popular questions from this chapter

For each of the questions, four choices have been provided. Select the correct alternative. Energy of an electron in a particular orbit of single electron species of beryllium is the same as the energy of an electron in the ground state of hydrogen atom. Identify the orbit of beryllium. (a) 1 (b) 2 (c) 3 (d) 4

For each of the questions, four choices have been provided. Select the correct alternative. The statements given below are the postulates of various atomic models. Arrange them in their chronological order. (1) Fine structure is due to the presence of subshells in the main energy level. (2) The size of an atom is much larger than the size of its nucleus. (3) As long as the electron is present in a particular orbit, its energy remains constant. (4) Negatively charged particles are uniformly spread in the lump of positive charge. (a) \(4,3,2,1\) (b) \(2,3,4,1\) (c) \(4,2,3,1\) (d) \(3,4,2,1\)

Match the entries given in column A with appropriate ones from column B. $$ \begin{array}{|l|ll|l|l|} {\text { Column A }} & {\text { Column B }} \\ \hline \text { A. } & \text { Be } & (\cdot) & \text { a. } & {[\mathrm{He}] 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6}} \\ \hline \text { B. } & \mathrm{Ne} & (\cdot) & \text { b. } & {[\mathrm{He}] 2 \mathrm{~s}^{2}} \\ \hline \text { C. } & \text { Si } & (\cdot) & \text { c. } & {[\mathrm{Ne}] 3 s^{2} 3 \mathrm{p}^{3}} \\ \hline \text { D. } & \mathrm{P} & (\cdot) & \text { d. } & {[\mathrm{Ne}] 3 s^{2} 3 \mathrm{p}^{5}} \\ \hline \text { E. } & \text { Cl } & (\cdot) & \text { e. } & {[\mathrm{Ne}] 3 s^{2} 3 \mathrm{p}^{2}} \\ \hline \end{array} $$

For each of the questions, four choices have been provided. Select the correct alternative. Zeeman and Stark effects can be explained by _______ quantum number. (a) principal (b) azimuthal (c) magnetic (d) spin

Direction for questions: State whether the following statements are true or false. Pairing of electrons in degenerate orbitals takes place only when the degenerate orbitals are filled with one electron each.
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