Atomic Structure Questions | Chemistry JEE Main Important Questions

Q 1 :

Match List I with List II

LIST I (Spectral Series for Hydrogen) LIST II (Spectral Region/Higher Energy State)

A. Lyman I. Infrared region

B. Balmer II. UV region

C. Paschen III. Infrared region

D. Pfund IV. Visible region

Choose the correct answer from the options given below: [2024]

A-I, B-III, C-II, D-IV
A-II, B-III, C-I, D-IV
A-II, B-IV, C-III, D-I
A-I, B-II, C-III, D-IV

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(3)

For hydrogen atom,

(i) Lyman series lies in ultraviolet region.

(ii) First four lines of Balmer series are in visible region and higher ones are in ultraviolet region.

(iii) Paschen and Pfund series are in infrared region.

Q 2 :

Number of spectral lines obtained in $H e^{+}$ spectra, when an electron makes transition from fifth excited state to first excited state will be _______ . [2024]

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(10)

Fifth excited state means sixth shell and first excited state means second shell. Thus transition is from 6th to 2nd shell. Number of spectral lines when electrons make transition from $n_{2}$ energy level to $n_{1}$ energy level in a sample of gas atoms is:

$\frac{(n_{2} - n_{1}) (n_{2} - n_{1} + 1)}{2} = \frac{(6 - 2) (6 - 2 + 1)}{2} = 10$

Q 3 :

Given below are two statements:

Statement I: A spectral line will be observed for a $2 p_{x} \to 2 p_{y}$ transition.

Statement II: $2 p_{x}$ and $2 p_{y}$ are degenerate orbitals.

In the light of the above statements, choose the correct answer from the options given below: [2025]

Both Statement I and Statement II are true
Statement I is true but Statement II is false
Both Statement I and Statement II are false
Statement I is false but Statement II is true

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(4)

Spectral line is observed when an electron makes a transition between two orbitals of different energy. As $2 p_{x}$ and $2 p_{y}$ have same energy (called degenerated orbitals), no spectral line is observed by transition of an electron between these two orbitals.

Q 4 :

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 $R_{H} = 10^{5} {cm}^{- 1},$ $h = 6.6 \times 10^{- 34} Js,$ $c = 3 \times 10^{8} m/s$ [2025]

Lyman series, $\infty \to 1$
Balmer series, $\infty \to 2$
Paschen series, $5 \to 3$
Paschen series, $\infty \to 3$

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(4)

$λ = 900 nm = 900 \times 10^{- 9} m$

$= 900 \times 10^{- 9} m \times 100 cm = 9 \times 10^{- 5} cm$

$R_{H} = 10^{5} {cm}^{- 1}$

By Rydberg’s equation:

$\frac{1}{λ} = R_{H} Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

$\frac{1}{9 \times 10^{- 5} cm} = 10^{5} {cm}^{- 1} \times {(1)}^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

$(\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) = \frac{1}{9}$

$n_{1} = 3, n_{2} = \infty$

Q 5 :

Electrons in a cathode ray tube have been emitted with a velocity of $1000$ ${ms}^{- 1}$ . The number of following statements which is/are true about the emitted radiation is ________ .

Given: $h = 6 \times 10^{- 34} Js,$ $m_{e} = 9 \times 10^{- 31} kg$ [2023]

(A) The de Broglie wavelength of the electron emitted is 666.67 nm.

(B) The characteristics of electrons emitted depend upon the material of the electrodes of the cathode ray tube.

(C) The cathode rays start from cathode and move towards anode.

(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.

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(2)

Given mass of electron $= 9 \times 10^{- 31} kg$ ,

$h = 6 \times 10^{- 34} J/sec$

$Wavelength (λ) = \frac{h}{m_{e} v_{e}} = \frac{6 \times 10^{- 34}}{9 \times 10^{- 31} \times 10^{3}}$

$= \frac{2}{3} \times 10^{- 6} m$

$= 0.66667 \times 10^{- 6} m$

$= 666.67 \times 10^{- 9} m$

$= 666.67 nm$

Cathode rays do not depend on the nature of the gas and metal plate.

Q 6 :

The energy of one mole of photons of radiation of frequency $2 \times 10^{12} Hz$ in ${J mol}^{- 1}$ is _________. (Nearest Integer)

[Given: $h = 6.626 \times 10^{- 34} Js$ ]

[ $N_{A} = 6.022 \times 10^{23} {mol}^{- 1}$ ] [2023]

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(798)

$E = n h ν$

For one mole of photons,

$E = 6.022 \times 10^{23} \times 6.626 \times 10^{- 34} \times 2 \times 10^{12}$

$E = 798.03 J$

Q 7 :

The wavelength of an electron of kinetic energy $4.50 \times 10^{- 29} J$ is ________ $\times 10^{- 5} m$ . (Nearest integer)

Given: mass of electron is $9 \times 10^{- 31} kg,$ $h = 6.6 \times 10^{- 34} Js$ [2023]

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(7)

$λ = \frac{h}{\sqrt{2 m K.E.}} = \frac{6.6 \times 10^{- 34}}{\sqrt{2 \times 9.1 \times 10^{- 31} \times 4.5 \times 10^{- 29}}}$

$= \frac{6.6 \times 10^{- 34}}{9.04 \times 10^{- 30}} = 7.3 \times 10^{- 5} \approx 7 \times 10^{- 5} m$

Where, $λ = Wavelength of an electron$

$h = Planck's constant$

$m = mass of electron$

$K.E. = Kinetic energy of electron$

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