Test: Atomic & Molecular Physics - 1 - Physics MCQ

# Test: Atomic & Molecular Physics - 1 - Physics MCQ

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## 20 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Atomic & Molecular Physics - 1

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Test: Atomic & Molecular Physics - 1 - Question 1

### The radius of the first Bohr orbit in  for a μ-mesic (or muonic) atom is ( The masses of μ– -meson and proton are 207 times and 1836 times respectively the mass of electron).

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 1

The radius of the first orbit (n = 1) of a hydrogen like muonic atomtaking finite mass ofnucleus in consideration is
....(i) where μ is reduced mass.
The reduced mass of the muonic atom (formed by a μ-meson and a proton) is
, where m is the mass o f the electron.
Thus. equation (i) ⇒

Test: Atomic & Molecular Physics - 1 - Question 2

### The moment of inertia of the HCl molecule is 2.71 x 10-47 kg-m2. The most populated rotational level for the molecule at temperature of 600 K corresponds to

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 2

The value of rotational quantum number J tor the maximum populated rotational level for a molecule at a temperature T is given by J =, where B is rotational constant.

∴
= 4.5 - 0.5 =4.

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Test: Atomic & Molecular Physics - 1 - Question 3

### The magnetic moment of an election moving in a circular orbit of radius r about a proton is where =

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 3

The magnetic moment is given by
...(i)
For electron the required centripetal force comes from Coulombic attraction between nucleus and electron.
...(ii)
From equation (ii), equation (i) ⇒

Test: Atomic & Molecular Physics - 1 - Question 4

The normal Zeeman splitting in the mercury 4916 Å line in a magnetic field of 0.3 T is

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 4

The Zeeman splitting ....(i)
∵
∴ Equation (i) ⇒
⇒

Test: Atomic & Molecular Physics - 1 - Question 5

The common wave number difference in the two successive rotational lines is

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 5

Tlie commom wave number difference in the two successive rotational lives

Test: Atomic & Molecular Physics - 1 - Question 6

For high principal quantum number (n) for hydrogen atom the spacing between the neighbouring energy level is proportional to

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 6

The difference of energy between energy levels having principal quantum number n and (n + 1) is given by

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 7

The Lande g-factor for the 3P2 level of an atom is______________
(Round off to one decimal places)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 7

The Lande’s g-factor is defined as
...(i)
For 3P2, S = 1, L = 1, J = 2
Therefore, equation (i) ⇒

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 8

The Bohr model gives the value for the ionization potential of Be+++ ion as__________10-1 eV
(Round off to two decimal places)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 8

The ionization energy of Be+++ = Z2 x ionization energy of hydrogen atom
= (4)2x 13.6 e V = 16 x 13.6 eV = 217.6 eV.

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 9

The line width of a spectral line of 600 mil wavelength emitted from a level of a lifetime of 10-8  sec, is__________×10-15 m (up to two decimal places)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 9

Since,
For λ = 600 nm, the line width is given by

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 10

The radiations given offby the Hg atoms returning to their normal states were studied by Frank and Heitz and
a line was observed at 2573 Å. The excitation potential for Hg is________volt (upto one decimal place)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 10

The excitation potential is given by

= 4.9 volt.

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 11

The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment of
inertia of the AIH molecule is_______x 10-47 kg/m2. (upto two decimal places)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 11

Since,
, where I is the moment of inertia of the rotating molecule.
Therefore,

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 12

If the Kα -radiation o f Mo (Z = 42) lias a wavelength o f 0.71 A. the wavelength o f the corresponding radiation for Cu (Z = 29) is Å. (upto two decimal places)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 12

From Moseley's law to r Kα - line, we have
Therefore,
Therefore,

Test: Atomic & Molecular Physics - 1 - Question 13

The possible values of  is

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 13

The total angular momentum
Taking self dot product on both sides, we get
⇒
⇒
⇒

Test: Atomic & Molecular Physics - 1 - Question 14

A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom is

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 14

For posittronium atom reduced mass,

The Rydbery constant for positronium atom, RP is given by
...(1)
Now, the wavelength of Balmer first line   of positronium a tom is given by

....(2)
Similarly, for hydrogen atom, the wavelength of Balmer first line (ni = 3 to nf = 2) is given by

Now, the ratio of wavelengths of first line o f Balmer series o fpositronium a tom and hydrogen a tom is

Test: Atomic & Molecular Physics - 1 - Question 15

A sample of ordinary hydrogen  gas in a discharge tube was seen to emit the usual Balmer spectrum. On careful examination however, it was found that the Hα -line in the spectrum was split into two fine lines, one an intense line at 6562.80 Å and the other at 6561.01 Å. From this, one can conclude that the gas sample had a small impurity of

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 15

⇒
⇒ .....(i)
For  the -line is at 6562.80 Å. thus equation (i) implies with M = 1836 m, λ = 6562.80 Å;
...(ii)
For unknown impurity, the - line is at 6561.01 Å thus M = x x 1836 m (H ere, we have assum ed the m ass of nucleus of unknown impurity equal to x times mass of proton or hydrogen nucleus). λ = 6561.01 Å;
...(iii)
Now. dividing equation (ii) by (iii), we get 1.000272824
⇒
⇒
Hence, the mass o f nucleus is 2 times that of Out o f the given options, nucleus  has the mass equal to two times the nuclear mass of

Test: Atomic & Molecular Physics - 1 - Question 16

The gBe+ ion has a nucleus with spin  The possible values of the hypofine quantum number F for the 2S1/2 electric level are

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 16

For 2S1/2 electronic level:
For gBe+ ion, I = 3/2
The hyperfine quantum number F is defined as
with decrease o f unity.

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 17

An atomic magnetic dipole having orbital magnetic moment of 1 Bohr magneton is aligned parallel to a external magnetic field of 1 Tesla. The energy required to turn the dipole to align it antiparallel to the field is_________x 10-4 eV. (upto two decimal places)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 17

The potential energy of dipole
For parallel alignment, θ = 0°
...(i)
For antiparallel alignment, θ = 180°
...(ii)
The energy required to align the dipole in antiparallel direction to the field

Test: Atomic & Molecular Physics - 1 - Question 18

In the doublet splitting of the first excited state. 22P3/2 — 2 2P1/2 of He+ is 5.84 cm-1. the corresponding separation for H is

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 18

Since, doublet splitting of a one election atomic state arising due to spin orbit interaction is given by

Therefore,
Therefore,

Test: Atomic & Molecular Physics - 1 - Question 19

Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV, is

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 19

For H2, the reduced mass (μ)
Therefore, frequency of oscillation of the molecule is given by

For vibrational quantum number (n) corresponding to dissociation energy (Ediss), we have

⇒
⇒

*Answer can only contain numeric values
Test: Atomic & Molecular Physics - 1 - Question 20

If the exciting line in an experiment is 5460 Å and the stokes line is at 5520 Å. the wavelength (inÅ) of the antistokes line is__________Å. (should be an integer)

Detailed Solution for Test: Atomic & Molecular Physics - 1 - Question 20

Since, the stokes and the anti-stokes lines have the same wave number difference with respect to the exciting line. The w ave num ber o f the exciting line is v = and that of the stokes line is
Thus, the wave num ber displacement is
Therefore, the wave number corresponding to the antistokes line would be given by

The corresponding wavelength is

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