Grade 11 : Chemistry - Atom Structure (Set 4)

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Grade 11 : Chemistry - Atom Structure (Set 4)— Questions & Detailed Solutions

Nuclide Atomic Number ($Z$) Mass Number ($A$)
P 6 14
Q 7 15
R 8 16
S 6 12
Based on the table above, which group of nuclides represents isotones (species having the exact same number of neutrons)?

Nuclide	Atomic Number ($Z$)	Mass Number ($A$)
P	6	14
Q	7	15
R	8	16
S	6	12

(A)

P and S

(B)

P and Q only

(C)

P, Q, and R

(D)

Q and S

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Isotones are atoms of different elements having the same number of neutrons ($N = A - Z$).
For P: $N = 14 - 6 = 8$
For Q: $N = 15 - 7 = 8$
For R: $N = 16 - 8 = 8$
For S: $N = 12 - 6 = 6$
Thus, P, Q, and R all have 8 neutrons and are isotones.

According to Bohr's model of the hydrogen atom, the radius of the $n$-th orbit is given by $r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$.
Calculate the radius of the 3rd orbit ($n = 3$) for a $Li^{2+}$ ion ($Z = 3$).

(A)

0.529 \AA

(B)

1.587 \AA

(C)

4.761 \AA

(D)

0.176 \AA

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Using Bohr's formula for radius:
$$r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$$
For $Li^{2+}$, $Z = 3$ and $n = 3$:
$$r_3 = 0.529 \times \frac{3^2}{3} = 0.529 \times 3 = 1.587 \text{ \AA}$$

Deflection setup: Subatomic particles are passed through a uniform electric field between two charged plates (+ and -). Beam X bends toward the (+) plate, Beam Y bends toward the (-) plate, and Beam Z passes straight through without deflection.
Identify the subatomic particles present in Beam X, Beam Y, and Beam Z respectively.

(A)

Protons, Electrons, Neutrons

(B)

Electrons, Protons, Neutrons

(C)

Alpha particles, Beta particles, Gamma rays

(D)

Neutrons, Electrons, Protons

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Oppositely charged particles attract:
1. Beam X is attracted to the positive plate, so it consists of negatively charged electrons.
2. Beam Y is attracted to the negative plate, so it consists of positively charged protons.
3. Beam Z is undeflected, so it consists of neutral neutrons.

Light of frequency $\nu = 1.20 \times 10^{15} \text{ Hz}$ strikes a clean metallic surface. The work function of the metal is $W_0 = 3.30 \times 10^{-19} \text{ J}$. (Planck's constant $h = 6.63 \times 10^{-34} \text{ J s}$).
What is the maximum kinetic energy ($KE_{\text{max}}$) of the emitted photoelectrons?

(A)

$4.66 \times 10^{-19} \text{ J}$

(B)

$7.96 \times 10^{-19} \text{ J}$

(C)

$3.30 \times 10^{-19} \text{ J}$

(D)

$1.13 \times 10^{-18} \text{ J}$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: According to Einstein's photoelectric equation:
$$E_{\text{photon}} = h\nu = (6.63 \times 10^{-34} \text{ J s}) \times (1.20 \times 10^{15} \text{ s}^{-1}) = 7.956 \times 10^{-19} \text{ J}$$
$$KE_{\text{max}} = h\nu - W_0 = 7.956 \times 10^{-19} \text{ J} - 3.30 \times 10^{-19} \text{ J} = 4.656 \times 10^{-19} \text{ J} \approx 4.66 \times 10^{-19} \text{ J}$$

The energy of an electron in the $n$-th stationary orbit of a hydrogen-like species is given by $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}$.
What is the energy of an electron residing in the 2nd orbit ($n = 2$) of a helium ion ($He^+$)?

(A)

-54.4 eV

(B)

-27.2 eV

(C)

-13.6 eV

(D)

-3.4 eV

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: For $He^+$, $Z = 2$. For the 2nd orbit, $n = 2$.
$$E_2 = -13.6 \times \frac{2^2}{2^2} = -13.6 \times \frac{4}{4} = -13.6 \text{ eV}$$

Which of the following sets of quantum numbers $(n, l, m_l, m_s)$ is allowed for an electron occupying a $3d$ subshell?

(A)

$n = 3, l = 3, m_l = 0, m_s = +1/2$

(B)

$n = 3, l = 2, m_l = -2, m_s = -1/2$

(C)

$n = 3, l = 1, m_l = +2, m_s = +1/2$

(D)

$n = 2, l = 2, m_l = +1, m_s = -1/2$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: For a $3d$ orbital:
1. Principal quantum number $n = 3$.
2. Azimuthal quantum number $l = 2$ (since $s=0, p=1, d=2$).
3. Magnetic quantum number $m_l$ can take values from $-l$ to $+l$, i.e., $\{-2, -1, 0, +1, +2\}$.
4. Spin quantum number $m_s = \pm 1/2$.
Option B satisfies all constraints ($n=3, l=2, m_l=-2, m_s=-1/2$).

An electron ($m = 9.1 \times 10^{-31} kg$) is accelerated to a speed of $1.0 \times 10^6 m/s$. ($h = 6.63 \times 10^{-34} \text{ kg m}^2/\text{s}$).
Calculate the de Broglie wavelength associated with this moving electron.

(A)

$7.29 \times 10^{-10} m$

(B)

$6.03 \times 10^{-10} m$

(C)

$1.37 \times 10^{-9} m$

(D)

$3.55 \times 10^{-11} m$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: De Broglie equation: $\lambda = \frac{h}{m v}$
$$\lambda = \frac{6.63 \times 10^{-34} \text{ kg m}^2/\text{s}}{(9.1 \times 10^{-31} \text{ kg}) \times (1.0 \times 10^6 \text{ m/s})} = \frac{6.63 \times 10^{-34}}{9.1 \times 10^{-25}} \approx 7.29 \times 10^{-10} \text{ m}$$

The uncertainty in the position of a microscopic particle of mass $1.0 \times 10^{-27} kg$ is $1.0 \times 10^{-10} m$. ($h = 6.626 \times 10^{-34} \text{ J s}$).
Using Heisenberg's Uncertainty Principle ($\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$), calculate the minimum uncertainty in its velocity ($\Delta v$).

(A)

527 m/s

(B)

52.7 m/s

(C)

$5.27 \times 10^4 m/s$

(D)

0.527 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: Heisenberg's relation: $\Delta x \cdot m \Delta v \ge \frac{h}{4\pi}$
$$\Delta v = \frac{h}{4\pi m \Delta x} = \frac{6.626 \times 10^{-34}}{4 \times 3.1416 \times 1.0 \times 10^{-27} \times 1.0 \times 10^{-10}}$$
$$\Delta v = \frac{6.626 \times 10^{-34}}{1.2566 \times 10^{-36}} \approx 527.3 \text{ m/s} \approx 527 \text{ m/s}$$

How many radial nodes and angular nodes does a $4p$ atomic orbital possess?

(A)

1 radial node and 2 angular nodes

(B)

2 radial nodes and 1 angular node

(C)

3 radial nodes and 1 angular node

(D)

2 radial nodes and 2 angular nodes

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: For a $4p$ orbital: $n = 4$ and $l = 1$.
1. Radial nodes = $n - l - 1 = 4 - 1 - 1 = 2$.
2. Angular nodes = $l = 1$.
Therefore, a $4p$ orbital has 2 radial nodes and 1 angular node.

Q10

Chromium (Cr, $Z = 24$) exhibits an anomalous ground-state electronic configuration due to extra stability of half-filled subshells: $[Ar] 3d^5 4s^1$.
How many total unpaired electrons are present in a neutral ground-state Chromium atom?

(A)

(B)

(C)

(D)

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Ground-state configuration of Cr ($Z=24$) is $1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^1$.
The $3d$ subshell has 5 orbitals with 1 unpaired electron each = 5 unpaired electrons.
The $4s$ subshell has 1 unpaired electron.
Total unpaired electrons = $5 + 1 = 6$.

Q11

An excited electron in a hydrogen atom transitions from energy level $n_2 = 5$ to ground state level $n_1 = 1$.
What is the total maximum number of spectral lines emitted during de-excitation?

(A)

(B)

(C)

(D)

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Total number of spectral lines emitted during transition from $n_2$ to $n_1$ is given by:
$$N = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2}$$
For $n_2 = 5$ and $n_1 = 1$:
$$N = \frac{(5 - 1)(5 - 1 + 1)}{2} = \frac{4 \times 5}{2} = 10 \text{ lines}$$

Q12

Consider a ground-state Iron atom (Fe, $Z = 26$) with electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2$.
What is the maximum number of electrons in a ground-state Fe atom that can have a spin quantum number $m_s = +1/2$?

(A)

(B)

(C)

(D)

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Fully paired subshells ($1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2$) contain 20 electrons $\implies 10$ with $m_s = +1/2$.
In $3d^6$, by Hund's rule, 5 orbitals contain 5 parallel spin-up ($+1/2$) electrons and 1 spin-down ($-1/2$) electron.
Maximum electrons with $m_s = +1/2$ = $10 + 5 = 15$.

Q13

In Bohr's atomic model, electron velocity in the $n$-th orbit is given by $v_n \propto \frac{Z}{n}$.
What is the ratio of the velocity of an electron in the 1st orbit ($n = 1$) to that in the 3rd orbit ($n = 3$) of a hydrogen atom?

(A)

$1 : 3$

(B)

$3 : 1$

(C)

$9 : 1$

(D)

$1 : 9$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Since $v_n \propto \frac{1}{n}$ for a given atom ($Z=1$):
$$\frac{v_1}{v_3} = \frac{1/1}{1/3} = \frac{3}{1} = 3 : 1$$

Q14

A radiation source emits light at a frequency of $\nu = 5.0 \times 10^{14} \text{ Hz}$. ($h = 6.626 \times 10^{-34} \text{ J s}$, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$).
Calculate the energy contained in 1 mole of photons of this electromagnetic radiation.

(A)

199.5 kJ/mol

(B)

$3.31 \times 10^{-19} \text{ kJ/mol}$

(C)

19.95 kJ/mol

(D)

331.3 kJ/mol

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: Energy per mole of photons:
$$E = N_A h \nu$$
$$E = (6.022 \times 10^{23} \text{ mol}^{-1}) \times (6.626 \times 10^{-34} \text{ J s}) \times (5.0 \times 10^{14} \text{ s}^{-1})$$
$$E = 19.95 \times 10^4 \text{ J/mol} = 199.5 \text{ kJ/mol}$$

Q15

Species Atomic Number ($Z$) Charge Total Electrons
$N^{3-}$ 7 -3 10
$Na^+$ 11 +1 10
$Al^{3+}$ 13 +3 10
$Mg^+$ 12 +1 11
Which of the species listed in the table is NOT isoelectronic with the others?

Species	Atomic Number ($Z$)	Charge	Total Electrons
$N^{3-}$	7	-3	10
$Na^+$	11	+1	10
$Al^{3+}$	13	+3	10
$Mg^+$	12	+1	11

(A)

$N^{3-}$

(B)

$Na^+$

(C)

$Al^{3+}$

(D)

$Mg^+$

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation: Isoelectronic species have equal numbers of electrons.
$N^{3-} (7+3=10)$, $Na^+ (11-1=10)$, and $Al^{3+} (13-3=10)$ all have 10 electrons.
$Mg^+$ has $12 - 1 = 11$ electrons, so it is NOT isoelectronic with the group.

Q16

A sodium street lamp emits yellow light with a wavelength $\lambda = 589 \text{ nm}$.
What is the wave number ($\bar{\nu}$) of this yellow light expressed in $cm^{-1}$?

(A)

$1.70 \times 10^4 cm^{-1}$

(B)

$1.70 \times 10^6 cm^{-1}$

(C)

$5.89 \times 10^4 cm^{-1}$

(D)

$1.70 \times 10^2 cm^{-1}$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: Wave number $\bar{\nu} = \frac{1}{\lambda}$.
Convert wavelength to centimeters: $\lambda = 589 \text{ nm} = 589 \times 10^{-7} cm$.
$$\bar{\nu} = \frac{1}{589 \times 10^{-7} \text{ cm}} \approx 16977.9 \text{ cm}^{-1} \approx 1.70 \times 10^4 \text{ cm}^{-1}$$

Q17

Orbital angular momentum of an electron is given by $L = \sqrt{l(l+1)} \frac{h}{2\pi}$.
What is the orbital angular momentum of an electron present in a $4d$ subshell?

(A)

$\sqrt{2} \frac{h}{2\pi}$

(B)

$\sqrt{6} \frac{h}{2\pi}$

(C)

$\sqrt{12} \frac{h}{2\pi}$

(D)

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: For a $d$ orbital, azimuthal quantum number $l = 2$.
Substituting $l = 2$ into the angular momentum equation:
$$L = \sqrt{2(2+1)} \frac{h}{2\pi} = \sqrt{6} \frac{h}{2\pi}$$

Q18

A $d_{xy}$ orbital consists of four lobes located in the xy-plane between the x and y axes.
How many nodal planes (planes where electron probability density is zero) exist for a $d_{xy}$ orbital?

(A)

(B)

(C)

(D)

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: The number of nodal planes (angular nodes) equals the azimuthal quantum number $l$.
For $d$ orbitals, $l = 2$. Specifically for $d_{xy}$, the two nodal planes are the xz-plane ($y=0$) and yz-plane ($x=0$). Thus, there are 2 nodal planes.

Q19

Monochromatic light of frequency $3\nu_0$ shines on a metal surface whose threshold frequency is $\nu_0$.
What is the ratio of the maximum kinetic energy of the emitted photoelectrons to the work function ($W_0$) of the metal?

(A)

$1 : 1$

(B)

$2 : 1$

(C)

$3 : 1$

(D)

$1 : 2$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Work function $W_0 = h\nu_0$.
Maximum Kinetic Energy $KE_{\text{max}} = h\nu - W_0 = h(3\nu_0) - h\nu_0 = 2h\nu_0$.
Ratio $\frac{KE_{\text{max}}}{W_0} = \frac{2h\nu_0}{h\nu_0} = \frac{2}{1} = 2 : 1$.

Q20

Consider the following electronic configurations for a 11-electron species:
State I: $1s^2 2s^2 2p^6 3s^1$
State II: $1s^2 2s^2 2p^5 3s^2$
State III: $1s^2 2s^2 2p^6 3p^1$
Which of the state(s) represent an excited electronic state for a neutral Sodium (Na) atom?

(A)

State I only

(B)

Both State II and State III

(C)

State II only

(D)

State III only

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Ground state of Na ($Z=11$) is State I ($1s^2 2s^2 2p^6 3s^1$).
State II ($1s^2 2s^2 2p^5 3s^2$) promotes a $2p$ electron to $3s$.
State III ($1s^2 2s^2 2p^6 3p^1$) promotes a $3s$ electron to $3p$.
Both State II and State III represent valid excited states of Sodium.

Grade 11 : Chemistry - Atom Structure (Set 4)

Grade 11 : Chemistry - Atom Structure (Set 4)— Questions & Detailed Solutions

Nuclide Atomic Number ($Z$) Mass Number ($A$)
P 6 14
Q 7 15
R 8 16
S 6 12
Based on the table above, which group of nuclides represents isotones (species having the exact same number of neutrons)?

According to Bohr's model of the hydrogen atom, the radius of the $n$-th orbit is given by $r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$.
Calculate the radius of the 3rd orbit ($n = 3$) for a $Li^{2+}$ ion ($Z = 3$).

The energy of an electron in the $n$-th stationary orbit of a hydrogen-like species is given by $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}$.
What is the energy of an electron residing in the 2nd orbit ($n = 2$) of a helium ion ($He^+$)?

Which of the following sets of quantum numbers $(n, l, m_l, m_s)$ is allowed for an electron occupying a $3d$ subshell?

An electron ($m = 9.1 \times 10^{-31} kg$) is accelerated to a speed of $1.0 \times 10^6 m/s$. ($h = 6.63 \times 10^{-34} \text{ kg m}^2/\text{s}$).
Calculate the de Broglie wavelength associated with this moving electron.

How many radial nodes and angular nodes does a $4p$ atomic orbital possess?

Chromium (Cr, $Z = 24$) exhibits an anomalous ground-state electronic configuration due to extra stability of half-filled subshells: $[Ar] 3d^5 4s^1$.
How many total unpaired electrons are present in a neutral ground-state Chromium atom?

An excited electron in a hydrogen atom transitions from energy level $n_2 = 5$ to ground state level $n_1 = 1$.
What is the total maximum number of spectral lines emitted during de-excitation?

Consider a ground-state Iron atom (Fe, $Z = 26$) with electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2$.
What is the maximum number of electrons in a ground-state Fe atom that can have a spin quantum number $m_s = +1/2$?

In Bohr's atomic model, electron velocity in the $n$-th orbit is given by $v_n \propto \frac{Z}{n}$.
What is the ratio of the velocity of an electron in the 1st orbit ($n = 1$) to that in the 3rd orbit ($n = 3$) of a hydrogen atom?

A radiation source emits light at a frequency of $\nu = 5.0 \times 10^{14} \text{ Hz}$. ($h = 6.626 \times 10^{-34} \text{ J s}$, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$).
Calculate the energy contained in 1 mole of photons of this electromagnetic radiation.

Species Atomic Number ($Z$) Charge Total Electrons
$N^{3-}$ 7 -3 10
$Na^+$ 11 +1 10
$Al^{3+}$ 13 +3 10
$Mg^+$ 12 +1 11
Which of the species listed in the table is NOT isoelectronic with the others?

A sodium street lamp emits yellow light with a wavelength $\lambda = 589 \text{ nm}$.
What is the wave number ($\bar{\nu}$) of this yellow light expressed in $cm^{-1}$?

Orbital angular momentum of an electron is given by $L = \sqrt{l(l+1)} \frac{h}{2\pi}$.
What is the orbital angular momentum of an electron present in a $4d$ subshell?

A $d_{xy}$ orbital consists of four lobes located in the xy-plane between the x and y axes.
How many nodal planes (planes where electron probability density is zero) exist for a $d_{xy}$ orbital?

Monochromatic light of frequency $3\nu_0$ shines on a metal surface whose threshold frequency is $\nu_0$.
What is the ratio of the maximum kinetic energy of the emitted photoelectrons to the work function ($W_0$) of the metal?

Consider the following electronic configurations for a 11-electron species:
State I: $1s^2 2s^2 2p^6 3s^1$
State II: $1s^2 2s^2 2p^5 3s^2$
State III: $1s^2 2s^2 2p^6 3p^1$
Which of the state(s) represent an excited electronic state for a neutral Sodium (Na) atom?

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Grade 11 : Chemistry - Atom Structure (Set 4)

Grade 11 : Chemistry - Atom Structure (Set 4)— Questions & Detailed Solutions

NuclideAtomic Number ($Z$)Mass Number ($A$)P614Q715R816S612Based on the table above, which group of nuclides represents isotones (species having the exact same number of neutrons)?

According to Bohr's model of the hydrogen atom, the radius of the $n$-th orbit is given by $r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$.Calculate the radius of the 3rd orbit ($n = 3$) for a $Li^{2+}$ ion ($Z = 3$).

The energy of an electron in the $n$-th stationary orbit of a hydrogen-like species is given by $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}$.What is the energy of an electron residing in the 2nd orbit ($n = 2$) of a helium ion ($He^+$)?

Which of the following sets of quantum numbers $(n, l, m_l, m_s)$ is allowed for an electron occupying a $3d$ subshell?

An electron ($m = 9.1 \times 10^{-31} kg$) is accelerated to a speed of $1.0 \times 10^6 m/s$. ($h = 6.63 \times 10^{-34} \text{ kg m}^2/\text{s}$).Calculate the de Broglie wavelength associated with this moving electron.

How many radial nodes and angular nodes does a $4p$ atomic orbital possess?

Chromium (Cr, $Z = 24$) exhibits an anomalous ground-state electronic configuration due to extra stability of half-filled subshells: $[Ar] 3d^5 4s^1$.How many total unpaired electrons are present in a neutral ground-state Chromium atom?

An excited electron in a hydrogen atom transitions from energy level $n_2 = 5$ to ground state level $n_1 = 1$.What is the total maximum number of spectral lines emitted during de-excitation?

Consider a ground-state Iron atom (Fe, $Z = 26$) with electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2$.What is the maximum number of electrons in a ground-state Fe atom that can have a spin quantum number $m_s = +1/2$?

In Bohr's atomic model, electron velocity in the $n$-th orbit is given by $v_n \propto \frac{Z}{n}$.What is the ratio of the velocity of an electron in the 1st orbit ($n = 1$) to that in the 3rd orbit ($n = 3$) of a hydrogen atom?

A radiation source emits light at a frequency of $\nu = 5.0 \times 10^{14} \text{ Hz}$. ($h = 6.626 \times 10^{-34} \text{ J s}$, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$).Calculate the energy contained in 1 mole of photons of this electromagnetic radiation.

SpeciesAtomic Number ($Z$)ChargeTotal Electrons$N^{3-}$7-310$Na^+$11+110$Al^{3+}$13+310$Mg^+$12+111Which of the species listed in the table is NOT isoelectronic with the others?

A sodium street lamp emits yellow light with a wavelength $\lambda = 589 \text{ nm}$.What is the wave number ($\bar{\nu}$) of this yellow light expressed in $cm^{-1}$?

Orbital angular momentum of an electron is given by $L = \sqrt{l(l+1)} \frac{h}{2\pi}$.What is the orbital angular momentum of an electron present in a $4d$ subshell?

A $d_{xy}$ orbital consists of four lobes located in the xy-plane between the x and y axes.How many nodal planes (planes where electron probability density is zero) exist for a $d_{xy}$ orbital?

Monochromatic light of frequency $3\nu_0$ shines on a metal surface whose threshold frequency is $\nu_0$.What is the ratio of the maximum kinetic energy of the emitted photoelectrons to the work function ($W_0$) of the metal?

Consider the following electronic configurations for a 11-electron species:State I: $1s^2 2s^2 2p^6 3s^1$State II: $1s^2 2s^2 2p^5 3s^2$State III: $1s^2 2s^2 2p^6 3p^1$Which of the state(s) represent an excited electronic state for a neutral Sodium (Na) atom?

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Nuclide Atomic Number ($Z$) Mass Number ($A$)
P 6 14
Q 7 15
R 8 16
S 6 12
Based on the table above, which group of nuclides represents isotones (species having the exact same number of neutrons)?

According to Bohr's model of the hydrogen atom, the radius of the $n$-th orbit is given by $r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$.
Calculate the radius of the 3rd orbit ($n = 3$) for a $Li^{2+}$ ion ($Z = 3$).

The energy of an electron in the $n$-th stationary orbit of a hydrogen-like species is given by $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}$.
What is the energy of an electron residing in the 2nd orbit ($n = 2$) of a helium ion ($He^+$)?

An electron ($m = 9.1 \times 10^{-31} kg$) is accelerated to a speed of $1.0 \times 10^6 m/s$. ($h = 6.63 \times 10^{-34} \text{ kg m}^2/\text{s}$).
Calculate the de Broglie wavelength associated with this moving electron.

Chromium (Cr, $Z = 24$) exhibits an anomalous ground-state electronic configuration due to extra stability of half-filled subshells: $[Ar] 3d^5 4s^1$.
How many total unpaired electrons are present in a neutral ground-state Chromium atom?

An excited electron in a hydrogen atom transitions from energy level $n_2 = 5$ to ground state level $n_1 = 1$.
What is the total maximum number of spectral lines emitted during de-excitation?

Consider a ground-state Iron atom (Fe, $Z = 26$) with electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2$.
What is the maximum number of electrons in a ground-state Fe atom that can have a spin quantum number $m_s = +1/2$?

In Bohr's atomic model, electron velocity in the $n$-th orbit is given by $v_n \propto \frac{Z}{n}$.
What is the ratio of the velocity of an electron in the 1st orbit ($n = 1$) to that in the 3rd orbit ($n = 3$) of a hydrogen atom?

A radiation source emits light at a frequency of $\nu = 5.0 \times 10^{14} \text{ Hz}$. ($h = 6.626 \times 10^{-34} \text{ J s}$, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$).
Calculate the energy contained in 1 mole of photons of this electromagnetic radiation.

Species Atomic Number ($Z$) Charge Total Electrons
$N^{3-}$ 7 -3 10
$Na^+$ 11 +1 10
$Al^{3+}$ 13 +3 10
$Mg^+$ 12 +1 11
Which of the species listed in the table is NOT isoelectronic with the others?

A sodium street lamp emits yellow light with a wavelength $\lambda = 589 \text{ nm}$.
What is the wave number ($\bar{\nu}$) of this yellow light expressed in $cm^{-1}$?

Orbital angular momentum of an electron is given by $L = \sqrt{l(l+1)} \frac{h}{2\pi}$.
What is the orbital angular momentum of an electron present in a $4d$ subshell?

A $d_{xy}$ orbital consists of four lobes located in the xy-plane between the x and y axes.
How many nodal planes (planes where electron probability density is zero) exist for a $d_{xy}$ orbital?

Monochromatic light of frequency $3\nu_0$ shines on a metal surface whose threshold frequency is $\nu_0$.
What is the ratio of the maximum kinetic energy of the emitted photoelectrons to the work function ($W_0$) of the metal?

Consider the following electronic configurations for a 11-electron species:
State I: $1s^2 2s^2 2p^6 3s^1$
State II: $1s^2 2s^2 2p^5 3s^2$
State III: $1s^2 2s^2 2p^6 3p^1$
Which of the state(s) represent an excited electronic state for a neutral Sodium (Na) atom?