The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.

( $\mathrm{R}=$ Rydberg constant)

Figure 1. electron probability density for 2 s orbital

Figure 2. wave function for 2s orbital

Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1?

The wavelength of spectral line obtained in the spectrum of $\mathrm{Li}^{2+}$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2 , is

The work functions of two metals $\left(\mathrm{M}_{\mathrm{A}}\right.$ and $\left.\mathrm{M}_{\mathrm{B}}\right)$ are in the $1: 2$ ratio. When these metals are exposed to photons of energy 6 eV , the kinetic energy of liberated electrons of $M_A: M_B$ is in the ratio of $2.642: 1$. The work functions (in eV ) of $M_A$ and $M_B$ are respectively.

Identify the INCORRECT statements from the following :

A. Notation ${ }_{12}^{24} \mathrm{Mg}$ represents 24 protons and 12 neutrons.

B. Wavelength of a radiation of frequency $4.5 \times 10^{15} \mathrm{~s}^{-1}$ is $6.7 \times 10^{-8} \mathrm{~m}$.

C. One radiation has wavelength $=\lambda_1(900 \mathrm{~nm})$ and energy $=\mathrm{E}_1$. Other radiation has wavelength $=\lambda_2(300 \mathrm{~nm})$ and energy $=\mathrm{E}_2 \cdot \mathrm{E}_1: \mathrm{E}_2=3: 1$.

D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is $1.006 \times 10^{16}$.

Choose the correct answer from the options given below :

Given,

(A) $\mathrm{n}=5, \mathrm{~m}_1=-1$

(B) $\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}_1=-1, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$

The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

Which of the following statements regarding the energy of the stationary state is true in the following one - electron systems ?

The energy of first (lowest) Balmer line of H atom is $x \mathrm{~J}$. The energy (in J) of second Balmer line of H atom is :

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is $\_\_\_\_$ $\mathrm{J} \mathrm{mol}^{-1}$.

Given: $R_H=2.18 \times 10^{-11} \mathrm{ergs}$.

Consider the following spectral lines for atomic hydrogen :

A. First line of Paschen series

B. Second line of Balmer series

C. Third line of Paschen series

D. Fourth line of Bracket series

The correct arrangement of the above lines in ascending order of energy is :

Given below are two statements :

Statement I : When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies.

Statement II : The frequency of second line of Balmer series obtained from $\mathrm{He}^{+}$is equal to that of first line of Lyman series obtained from hydrogen atom.

In the light of the above statements, choose the correct answer from the options given below :

The Bohr radius of a hydrogen like species is 70.53 pm . The species and the stationary state (n) are respectively

(Given : Hydrogen atom Bohr radius is 52.9 pm )

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $\mathrm{He}^{+}$is:

$ \text { Match the LIST-I with LIST-II } $

Which of the following statement(s) is/are true ?

A. If two orbitals have the same value of ( $\mathrm{n}+l$ ), the orbital with lower value of n will have lower energy.

B. Energies of the orbitals in the same subshell increase with increase in atomic number.

C. The size of $2 \mathrm{p}_x$ orbital is less than the size of $3 \mathrm{p}_x$ orbital.

D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.

Choose the correct answer from the options given below :

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.

A. $n=3, l=2, m=+1$

B. $n=4, l=0, m=0$

C. $n=6, l=1, m=0$

D. $n=5, l=1, m=+1$

E. $n=2, l=1, m=+1$

Choose the correct answer from the options given below:

Identify the correct statements from the following :

A. Heisenberg uncertainty principle is applicable to electrons.

B. The size of $2 p_x$ orbital is less than the size of $3 p_x$ orbital.

C. The energy of 2 s orbital of H atom is equal to the energy of 2 s orbital of Li .

D. The electronic configuration of Cr is $[\mathrm{Ar}] 3 \mathrm{~d}^5 4 \mathrm{~s}^1$

Choose the correct answer from the options given below:

The species having identical radii according to the Bohr's theory are :

A. H (first orbit)

B. $\mathrm{He}^{+}$(first orbit)

C. $\mathrm{He}^{+}$(Second orbit)

D. $\mathrm{Li}^{2+}$ (first orbit)

E. $\mathrm{Be}^{3+}$ (Second orbit)

Choose the correct answer from the options given below :

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

Which of the following is correct set of 4 quantum numbers of $19^{\text {th }}$ electron in Chromium (Atomic number $=24$ ) in accordance with Aufbau principle?

What is the energy (in J atom⁻¹) required for the following process?

Li²⁺ (g) → Li³⁺ (g) + e⁻

(Take the ionization energy for the H atom in the ground state as $2.18 \times 10^{−18} \text{ J atom}^{−1}$)

Correct statements for an element with atomic number 9 are:

A. There can be 5 electrons for which $m_s = +\frac{1}{2}$ and 4 electrons for which $m_s = -\frac{1}{2}$.

B. There is only one electron in $p_z$ orbital.

C. The last electron goes to orbital with $n = 2$ and $l = 1$.

D. The sum of angular nodes of all the atomic orbitals is 1.

Choose the correct answer from the options given below:

The extra stability of half-filled subshell is due to :

(A) Symmetrical distribution of electrons

(B) Smaller coulombic repulsion energy

(C) The presence of electrons with the same spin in non-degenerate orbitals

(D) Larger exchange energy

(E) Relatively smaller shielding of electrons by one another

Indentify the correct statements :

Which of the following statements are correct, if the threshold frequency of caesium is $5.16 \times$ $10^{14} \mathrm{~Hz}$ ?

A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs , the ammeter shows the presence of current.

B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced.

C. When a red light is used instead of the yellow light, the current produced is higher with respect to the yellow light.

D. When a blue light is used, the ammeter shows the formation of current.

E. When a white light is used. the ammeter shows formation of current.

Choose the correct answer from the options given below:

Consider the ground state of chromium atom $(Z=24)$. How many electrons are with Azimuthal quantum number $l=1$ and $l=2$ respectively ?

Which one of the following about an electron occupying the 1 s orbital in a hydrogen atom is incorrect?

(Bohr's radius is represented by $\mathrm{a}_0$)

For electrons in ' 2 s ' and ' 2 p ' orbitals, the orbital angular momentum values, respectively are:

Which of the following statements are true?

(A) The subsidiary quantum number $l$ describes the shape of the orbital occupied by the electron.

(B) is the boundary surface diagram of the $2 \mathrm{p}_x$ orbital.

(C) The + and - signs in the wave function of the $2 p_x$ orbital refer to charge.

(D) The wave function of $2 \mathrm{p}_x$ orbital is zero everywhere in the $x y$ plane.

Choose the correct answer from the options given below :

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n?

[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]

Given below are two statements :

Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.

Statement (II) : If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is $\geqslant \sqrt{\frac{h}{\pi}} \times \frac{1}{2 m}$.

In the light of the above statements, choose the correct answer from the options given below :

If $a$₀ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer]

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?

(A) 1s < 2p < 3d < 4s

(B) 1s < 2s = 2p < 3s = 3p

(C) 1s < 2s < 2p < 3s < 3p

(D) 1s < 2s < 4s < 3d

Choose the correct answer from the options given below :

In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?

A. $\mathrm{n}=1, \mathrm{l}=0, \mathrm{~m}_1=0$

B. $\mathrm{n}=2, \mathrm{l}=0, \mathrm{~m}_1=0$

C. $\mathrm{n}=2, \mathrm{I}=1, \mathrm{~m}_1=1$

D. $\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}_1=1$

E. $\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}_1=0$

Choose the correct answer from the options given below:

For hydrogen atom, the orbital/s with lowest energy is/are :

(A) $\mathrm{4 s}$

(B) $3 \mathrm{p}_x$

(C) $3 \mathrm{~d}_{x^2-y^2}$

(D) $3 \mathrm{~d}_{z^2}$

(E) $4 \mathrm{p}_z$

Choose the correct answer from the options given below :

Given below are two statements :

Statement (I) : For a given shell, the total number of allowed orbitals is given by $n^2$.

Statement (II) : For any subshell, the spatial orientation of the orbitals is given by $-l$ to $+l$ values including zero.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements about X-ray spectra of elements :

Statement (I) : A plot of $\sqrt{v}$ ( $v=$ frequency of X-rays emitted) vs atomic mass is a straight line.

Statement (II) : A plot of $v(\nu=$ frequency of $X$-rays emitted) vs atomic number is a straight line. In the light of the above statements, choose the correct answer from the options given below :

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H atom is suitable for this?

Given : Rydberg constant $\left.\mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$

Given below are two statements :

Statement (I) : A spectral line will be observed for a $2 p_x \rightarrow 2 p_y$ transition.

Statement (II) : $2 \mathrm{p}_x$ and $2 \mathrm{p}_y$ are degenerate orbitals.

In the light of the above statements, choose the correct answer from the options given below :

Radius of the first excited state of Helium ion is given as : $\mathrm{a}_0 \rightarrow$ radius of first stationary state of hydrogen atom.

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency '$A$' $\times 10^{12}$ hertz and that has a radiant intensity in that direction of $\frac{1}{{ 'B'}}$, watt per steradian. '$A$' and '$B$' are respectively

Compare the energies of following sets of quantum numbers for multielectron system.

(A) $\mathrm{n}=4,1=1$

(B) $\mathrm{n}=4,1=2$

(C) $\mathrm{n}=3, \mathrm{l}=1$

(D) $\mathrm{n}=3,1=2$

(E) $\mathrm{n}=4,1=0$

Choose the correct answer from the options given below :

The incorrect postulates of the Dalton's atomic theory are :

(A) Atoms of different elements differ in mass.

(B) Matter consists of divisible atoms.

(C) Compounds are formed when atoms of different element combine in a fixed ratio.

(D) All the atoms of given element have different properties including mass.

(E) Chemical reactions involve reorganisation of atoms.

Choose the correct answer from the options given below :

Choose the Incorrect Statement about Dalton's Atomic Theory

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are

Given below are two statements :

Statement (I) : The orbitals having same energy are called as degenerate orbitals.

Statement (II) : In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.

In the light of the above statements, choose the most appropriate answer from the options given below :

Match List I with List II

Choose the correct answer from the options given below:

The correct set of four quantum numbers for the valence electron of rubidium atom $(\mathrm{Z}=37)$ is :

The energy of an electron in the first Bohr orbit of hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$. Its energy in the third Bohr orbit is ____________.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :

Assertion A : In the photoelectric effect, the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes the surface.

Reason R : When the photon of any energy strikes an electron in the atom, transfer of energy from the photon to the electron takes place.

In the light of the above statements, choose the most appropriate answer from the options given below :

Henry Moseley studied characteristic X-ray spectra of elements. The graph which represents his observation correctly is

Given $v=$ frequency of $\mathrm{X}$-ray emitted

Z = atomic number

If the radius of the first orbit of hydrogen atom is $\alpha_{0}$, then de Broglie's wavelength of electron in $3^{\text {rd }}$ orbit is :

Which one of the following sets of ions represents a collection of isoelectronic species?

(Given : Atomic Number : $\mathrm{F:9,Cl:17,Na=11,Mg=12,Al=13,K=19,Ca=20,Sc=21}$)

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $\mathrm{n=4}$ to $\mathrm{n}=2$ of $\mathrm{He}^{+}$ spectrum

The shortest wavelength of hydrogen atom in Lyman series is $\lambda$. The longest wavelength is Balmer series of He$^+$ is

The radius of the $\mathrm{2^{nd}}$ orbit of $\mathrm{Li^{2+}}$ is $x$. The expected radius of the $\mathrm{3^{rd}}$ orbit of $\mathrm{Be^{3+}}$ is

The number of s-electrons present in an ion with 55 protons in its unipositive state is

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power "n" i.e. ${v^n}$ of X-rays emitted is plotted against atomic number "Z", following graph is obtained.

The value of 'n' is :

Given below are the quantum numbers for 4 electrons.

A. $\mathrm{n}=3,l=2, \mathrm{~m}_{1}=1, \mathrm{~m}_{\mathrm{s}}=+1 / 2$

B. $\mathrm{n}=4,l=1, \mathrm{~m}_{1}=0, \mathrm{~m}_{\mathrm{s}}=+1 / 2$

C. $\mathrm{n}=4,l=2, \mathrm{~m}_{1}=-2, \mathrm{~m}_{\mathrm{s}}=-1 / 2$

D. $\mathrm{n}=3,l=1, \mathrm{~m}_{1}=-1, \mathrm{~m}_{\mathrm{s}}=+1 / 2$

The correct order of increasing energy is :

Given below are two statements: One is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion $\mathbf{A}$ : Zero orbital overlap is an out of phase overlap.

Reason $\mathbf{R}$ : It results due to different orientation / direction of approach of orbitals.

In the light of the above statements, choose the correct answer from the options given below

Identify the incorrect statement from the following.

The correct decreasing order of energy for the orbitals having, following set of quantum numbers :

(A) n = 3, l = 0, m = 0

(B) n = 4, l = 0, m = 0

(C) n = 3, l = 1, m = 0

(D) n = 3, l = 2, m = 1

is :

Outermost electronic configurations of four elements A, B, C, D are given below :

(A) $3 s^{2}$

(B) $3 s^{2} 3 p^{1}$

(C) $3 s^{2} 3 p^{3}$

(D) $3 s^{2} 3 p^{4}$

The correct order of first ionization enthalpy for them is :

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Energy of $2 \mathrm{s}$ orbital of hydrogen atom is greater than that of $2 \mathrm{s}$ orbital of lithium.

Reason R: Energies of the orbitals in the same subshell decrease with increase in the atomic number.

In the light of the above statements, choose the correct answer from the options given below.

Which of the following sets of quantum numbers is not allowed?

The number of radial nodes and total number of nodes in 4p orbital respectively are :

Which of the following is the correct plot for the probability density ${\psi ^2}$ (r) as a function of distance 'r' of the electron from the nucleus for 2s orbital?

Which of the following statements are correct?

(A) The electronic configuration of Cr is [Ar] 3d⁵ 4s¹.

(B) The magnetic quantum number may have a negative value.

(C) In the ground state of an atom, the orbitals are filled in order of their increasing energies.

(D) The total number of nodes are given by n $-$ 2.

Choose the most appropriate answer from the options given below :

Consider the following statements :

(A) The principal quantum number 'n' is a positive integer with values of 'n' = 1, 2, 3, ...

(B) The azimuthal quantum number 'l' for a given 'n' (principal quantum number) can have values as 'l' = 0, 1, 2, ...... n

(C) Magnetic orbital quantum number 'm_l' for a particular 'l' (azimuthal quantum number) has (2l + 1) values.

(D) $\pm$ 1/2 are the two possible orientations of electron spin.

(E) For l = 5, there will be a total of 9 orbital

Which of the above statements are correct?

The number of radial and angular nodes in 4d orbital are, respectively

If the radius of the 3^rd Bohr's orbit of hydrogen atom is r₃ and the radius of 4^th Bohr's orbit is r₄. Then :

The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is :

[Given : The threshold frequency of platinum is 1.3 $\times$ 10¹⁵ s^$-$1 and h = 6.6 $\times$ 10^$-$34 J s.]

The pair, in which ions are isoelectronic with AI³⁺ is :

The energy of one mole of photons of radiation of wavelength 300 nm is

(Given : h = 6.63 $\times$ 10^$-$34 J s, N_A = 6.02 $\times$ 10²³ mol^$-$1, c = 3 $\times$ 10⁸ m s^$-$1)

Consider the following pairs of electrons

(A) (a) n = 3, $l$ = 1, m₁ = 1, m_s = + ${1 \over 2}$

      (b) n = 3, 1 = 2, m₁ = 1, m_s = + ${1 \over 2}$

(B) (a) n = 3, $l$ = 2, m₁ = $-$2, m_s = $-$${1 \over 2}$

      (b) n = 3, $l$ = 2, m₁ = $-$1, m_s = $-$${1 \over 2}$

(C) (a) n = 4, $l$ = 2, m₁ = 2, m_s = + ${1 \over 2}$

      (b) n = 3, $l$ = 2, m₁ = 2, m_s = + ${1 \over 2}$

The pairs of electrons present in degenerate orbitals is/are :