Question 1

Which one of the following is the correct electronic configuration for carbon, which has 6 electrons?

Accepted Answer

The correct electronic configuration for carbon, which has 6 electrons, is $1 s ^ { 2 } 2 s ^ { 2 } 2 p ^ { 2 }$. This follows the Aufbau principle, filling the lowest energy levels first.

Question 2

In an excited hydrogen atom, the electron is in the $4 d$ state. If this atom is in an external magnetic field, what are the smallest and largest possible angles between the orbital angular momentum and the direction of the magnetic field (or any other direction, for that matter)?

Accepted Answer

The answer of In an excited hydrogen atom, the electron...

Question 3

What is the minimum angle between the $z$-axis (or any other axis you choose) and the orbital angular momentum of an electron in the $n = 4$ state?

Accepted Answer

The answer of What is the minimum angle between the...

Question 4

What is the electron configuration for Li, which has 3 electrons?

Accepted Answer

The electron configuration for lithium (Li), which has 3 electrons, is $1s^2 2s^1$. This configuration fills the 1s orbital with 2 electrons and places the third electron in the 2s orbital.

Question 5

A hydrogen atom is in the 6h state. Which one of the following numbers could be an orbital angular momentum quantum number ʆ for that state?

Accepted Answer

The orbital angular momentum quantum number $l$ can take on any integer value from 0 to $n-1$, where $n$ is the principal quantum number. For a hydrogen atom in the 6h state, $n=6$, so $l$ can be 0, 1, 2, 3, 4, or 5. Therefore, the only possible value from the given options is 5.

Question 6

A hydrogen atom is in the $6 h$ state. How many electrons are allowed in this state?

Accepted Answer

The answer of A hydrogen atom is in the \(6...

Question 7

In a hydrogen atom, a given electron has n = 7. How many possible values can ʆ have?

Accepted Answer

The quantum number ʆ (azimuthal or angular momentum quantum number) can have values from 0 to n-1. For n = 7, ʆ can be 0, 1, 2, 3, 4, 5, or 6, making 7 possible values.

Question 8

An atom has completely filled inner shells and a single valence electron in an excited $p$ state. The filled inner shells have an orbital momentum equal to zero. When a magnetic field is applied, what are the possible angles between the magnetic field and the orbital angular momentum?

Accepted Answer

The orbital angular momentum of a single electron in a $p$ state is $ \hbar $. When a magnetic field is applied, the electron's magnetic moment will align with the field, resulting in a precession of the electron's orbital angular momentum around the field. The possible angles between the magnetic field and the orbital angular momentum are given by the equation $ \cos \theta = \frac { m _ { l } } { l } $, where $ m _ { l } $ is the magnetic quantum number and $ l $ is the orbital angular momentum quantum number. For a single electron in a $p$ state, $ l = 1 $ and $ m _ { l } = -1, 0, 1 $. Therefore, the possible angles between the magnetic field and the orbital angular momentum are $ \theta = 45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ } $.

Question 9

What is the correct ground state electron configuration of boron, which has 5 electrons?

Accepted Answer

The correct ground state electron configuration for boron, which has 5 electrons, is $1 s ^ { 2 } 2 s ^ { 2 } 2 p ^ { 1 }$. This configuration fills the lowest energy levels first (1s, then 2s) before placing an electron in the 2p orbital.

Question 10

Which one of the following is the correct electronic configuration for the sodium atom, which has 11 electrons?

Accepted Answer

The correct electronic configuration for sodium (Na), which has 11 electrons, is $1 s ^ { 2 } 2 s ^ { 2 } 2 p ^{6} 3 s ^ { 1 }$. This follows the Aufbau principle, filling the lowest energy levels first.

Question 11

An atom with atomic number 6 is in its ground state. How many electrons are in its outermost shell?

Accepted Answer

The answer of An atom with atomic number 6 is...

Question 12

A hydrogen atom is in the 6h state. Which one of the following is not a magnetic quantum number for that state?

Accepted Answer

The magnetic quantum number (m_l) can range from -l to +l, where l is the azimuthal (or angular momentum) quantum number. For a hydrogen atom in the 6h state, the principal quantum number n=6, and the azimuthal quantum number l for an h state is 5 (since the sequence starts from 0: s=0, p=1, d=2, f=3, g=4, h=5). Therefore, m_l can range from -5 to +5, making 6 not a possible value for the magnetic quantum number in this state.

Question 13

In a hydrogen atom, a given electron has $\ell = 7$. How many possible values can $m _ { 1 }$ have?

Accepted Answer

The magnetic quantum number $m_l$ can take on integer values ranging from $-\ell$ to $+\ell$, including zero. Therefore, for $\ell = 7$, $m_l$ can be any integer between -7 and +7, giving a total of 15 possible values.

Question 14

What is the greatest magnitude of the orbital angular momentum $L$ that you can find in a state with $n = 6$ ?

Accepted Answer

The answer of What is the greatest magnitude of the...

Question 15

Consider the $n = 10$ shell.
(a) What is the largest value of the angular momentum quantum number, $l$, in this shell?
(b) How many electrons can be placed in this shell?

Accepted Answer

The answer of Consider the $n = 10$ shell.
(a) What...

Question 16

Write out the electron configuration for the ground state of the phosphorus atom, which has 15 electrons.

Accepted Answer

The answer of Write out the electron configuration for the...

Question 17

The only valid electron state and shell designation among the following is

Accepted Answer

The correct electron state and shell designation is $2 p , \mathrm {~L} ( n = 2 )$ shell. This is because the principal quantum number $n=2$ corresponds to the L shell, and the $p$ orbital is valid for $n=2$. Other options are incorrect due to mismatches in quantum numbers and orbital designations.

Question 18

In a hydrogen atom, an electron with n = 7 can exist in how many different quantum states?

Accepted Answer

The number of different quantum states for an electron in a hydrogen atom with principal quantum number n = 7 is given by n^2. Therefore, for n = 7, the number of different quantum states is 7^2 = 49. However, each state can have two different spin orientations (spin up or spin down), doubling the number of quantum states to 98.

Question 19

An atom has completely filled inner shells and a single valence electron in an excited p state. The filled inner shells have an orbital momentum equal to zero. What is the magnitude of the orbital angular momentum of the atom?

Accepted Answer

The answer of An atom has completely filled inner shells...

Question 20

The only invalid electron state and shell designation among the following is

Accepted Answer

The $d$ subshell does not exist in the $n = 2$ energy level. The first $d$ subshell appears in the $n = 3$ level.

Quiz 28: Quantum Mechanics of Atoms

Which one of the following is the correct electronic configuration for carbon, which has 6 electrons?

In an excited hydrogen atom, the electron is in the $4 d$ state. If this atom is in an external magnetic field, what are the smallest and largest possible angles between the orbital angular momentum and the direction of the magnetic field (or any other direction, for that matter)?

What is the minimum angle between the $z$ -axis (or any other axis you choose) and the orbital angular momentum of an electron in the $n = 4$ state?

What is the electron configuration for Li, which has 3 electrons?

A hydrogen atom is in the 6h state. Which one of the following numbers could be an orbital angular momentum quantum number ʆ for that state?

A hydrogen atom is in the $6 h$ state. How many electrons are allowed in this state?

In a hydrogen atom, a given electron has n = 7. How many possible values can ʆ have?

An atom has completely filled inner shells and a single valence electron in an excited $p$ state. The filled inner shells have an orbital momentum equal to zero. When a magnetic field is applied, what are the possible angles between the magnetic field and the orbital angular momentum?

What is the correct ground state electron configuration of boron, which has 5 electrons?

Which one of the following is the correct electronic configuration for the sodium atom, which has 11 electrons?

An atom with atomic number 6 is in its ground state. How many electrons are in its outermost shell?

A hydrogen atom is in the 6h state. Which one of the following is not a magnetic quantum number for that state?

In a hydrogen atom, a given electron has $\ell = 7$ . How many possible values can $m _ { 1 }$ have?

What is the greatest magnitude of the orbital angular momentum $L$ that you can find in a state with $n = 6$ ?

Consider the $n = 10$ shell. (a) What is the largest value of the angular momentum quantum number, $l$ , in this shell? (b) How many electrons can be placed in this shell?

Write out the electron configuration for the ground state of the phosphorus atom, which has 15 electrons.

The only valid electron state and shell designation among the following is

In a hydrogen atom, an electron with n = 7 can exist in how many different quantum states?

An atom has completely filled inner shells and a single valence electron in an excited p state. The filled inner shells have an orbital momentum equal to zero. What is the magnitude of the orbital angular momentum of the atom?

The only invalid electron state and shell designation among the following is

Quiz 28: Quantum Mechanics of Atoms

Which one of the following is the correct electronic configuration for carbon, which has 6 electrons?

In an excited hydrogen atom, the electron is in the 4d4 d4d state. If this atom is in an external magnetic field, what are the smallest and largest possible angles between the orbital angular momentum and the direction of the magnetic field (or any other direction, for that matter)?

What is the minimum angle between the zzz -axis (or any other axis you choose) and the orbital angular momentum of an electron in the n=4n = 4n=4 state?

What is the electron configuration for Li, which has 3 electrons?

A hydrogen atom is in the 6h state. Which one of the following numbers could be an orbital angular momentum quantum number ʆ for that state?

A hydrogen atom is in the 6h6 h6h state. How many electrons are allowed in this state?

In a hydrogen atom, a given electron has n = 7. How many possible values can ʆ have?

An atom has completely filled inner shells and a single valence electron in an excited ppp state. The filled inner shells have an orbital momentum equal to zero. When a magnetic field is applied, what are the possible angles between the magnetic field and the orbital angular momentum?

What is the correct ground state electron configuration of boron, which has 5 electrons?

Which one of the following is the correct electronic configuration for the sodium atom, which has 11 electrons?

An atom with atomic number 6 is in its ground state. How many electrons are in its outermost shell?

A hydrogen atom is in the 6h state. Which one of the following is not a magnetic quantum number for that state?

In a hydrogen atom, a given electron has ℓ=7\ell = 7ℓ=7 . How many possible values can m1m _ { 1 }m1​ have?

What is the greatest magnitude of the orbital angular momentum LLL that you can find in a state with n=6n = 6n=6 ?

Consider the n=10n = 10n=10 shell. (a) What is the largest value of the angular momentum quantum number, lll , in this shell? (b) How many electrons can be placed in this shell?

Write out the electron configuration for the ground state of the phosphorus atom, which has 15 electrons.

The only valid electron state and shell designation among the following is

In a hydrogen atom, an electron with n = 7 can exist in how many different quantum states?

An atom has completely filled inner shells and a single valence electron in an excited p state. The filled inner shells have an orbital momentum equal to zero. What is the magnitude of the orbital angular momentum of the atom?

The only invalid electron state and shell designation among the following is

In an excited hydrogen atom, the electron is in the $4 d$ state. If this atom is in an external magnetic field, what are the smallest and largest possible angles between the orbital angular momentum and the direction of the magnetic field (or any other direction, for that matter)?

What is the minimum angle between the $z$ -axis (or any other axis you choose) and the orbital angular momentum of an electron in the $n = 4$ state?

A hydrogen atom is in the $6 h$ state. How many electrons are allowed in this state?

An atom has completely filled inner shells and a single valence electron in an excited $p$ state. The filled inner shells have an orbital momentum equal to zero. When a magnetic field is applied, what are the possible angles between the magnetic field and the orbital angular momentum?

In a hydrogen atom, a given electron has $\ell = 7$ . How many possible values can $m _ { 1 }$ have?

What is the greatest magnitude of the orbital angular momentum $L$ that you can find in a state with $n = 6$ ?

Consider the $n = 10$ shell. (a) What is the largest value of the angular momentum quantum number, $l$ , in this shell? (b) How many electrons can be placed in this shell?