Test: Combined (Atomic + Nuclear + Solid) - Physics MCQ

# Test: Combined (Atomic + Nuclear + Solid) - Physics MCQ

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## 30 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Combined (Atomic + Nuclear + Solid)

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Test: Combined (Atomic + Nuclear + Solid) - Question 1

### For a 3-D free electron gas, the electron density n and the Fermi energy EF, are related as

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 1

Fermi energy for 3-D free electron gas

Test: Combined (Atomic + Nuclear + Solid) - Question 2

### The tight binding energy dispersion relation for electrons in 1-D array of a toms having lattice constant a and total length l is E = E0 + γ cosh (ka) . where E0, γ are constants and k is wave vector. Which graph best represents the variation of effective mass with energy.

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 2

E = E0 + γ cosh (ka)

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Test: Combined (Atomic + Nuclear + Solid) - Question 3

### The magnetization (M) of some hypothetical substance in magnetic field (H) is given by M (H) = C In2(H + H0), H > l - H0 where H0 and C are positive and negative constants respectively. In what category should tliis substance be put

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 3

X is always positive and shows saturation for higher values of H.
Hence, die namre of the substance is paramagnetic.

Test: Combined (Atomic + Nuclear + Solid) - Question 4

The temperature at which the probability that an energy state with an energy 0.2 e V above the fenni level will be occupied by an electron is 10 %

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 4

Test: Combined (Atomic + Nuclear + Solid) - Question 5

The dispersion relation of phonons in a solid is given by

Tlie velocity of phonons at large wavelength is related to wave number k as

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 5

Forlargewavelength kxa, kya, kza ≪ 1

Test: Combined (Atomic + Nuclear + Solid) - Question 6

Consider a crystal with base-centered-cubic lattice with positions of basis atoms at (0, 0, 0) and
The lattice plane for which there is no diffraction peak is

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 6

Structure factor
‘S' is non-zero only if (v1 + v2) is even and there is no condition for v3
If (v1 + v2) is odd. there will be no diffraction peak.
For plane (1 2 0). v1 + v2 = 3 (odd)
Hence, for plane (1 2 0). there is no diffraction peak.

Test: Combined (Atomic + Nuclear + Solid) - Question 7

In nearly free election model, the wavefimctions at the Biillonin zone boimclaiy are  and ,  normalized over unit length of line. If potential energy ofan electron in the crystal at point x is V (x) = V0 [1 - cos (2πx)] . the first order energy gap between two standing waves is

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 7

⇒ Eg = -V0

Test: Combined (Atomic + Nuclear + Solid) - Question 8

Ap-doped semiconductor slab carries a current I = 150 mA in a magnetic field 0.3 T as shown. Voltage differences Vx and Vy are 2.5 mV and 0.3 mV, respectively. The mobility of majority charge earners is 0.8 m2 V-1 sec-1. The current density in mA/m2 is

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 8

Test: Combined (Atomic + Nuclear + Solid) - Question 9

Distance of a point inside a superconductor from the surface, at which the magnetic field is two-third of its value at the surface, in terms of London penetration depth (λ) is

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 9

Bz (x) = Bz = (0)e -x/λ, λ is London penetration depth.
Given that at some depth x.

*Answer can only contain numeric values
Test: Combined (Atomic + Nuclear + Solid) - Question 10

Inteiplanar distance of a plane passing through points (0,0,1), (1,0,0) and  in a crystal with lattice constant 2Å is _________ Å. (Upto two decim al places)

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 10

Plane passing through these points is (1 1 0)

*Answer can only contain numeric values
Test: Combined (Atomic + Nuclear + Solid) - Question 11

Critical magnetic fields of a superconductor at 2K and 6K is 13.5 mA /m and 4.5 mA /m respectively. The transition temperature of the superconductor is _________ K.
[Upto two decimal places]

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 11

From the relation between critical magnetic field and temperature

from the two relations, we can derive that

Putting T1 = 2K, T2 = 6K. Hc (T1) = 13.5 mA/m and H(T2) = 4.5 mA/m
⇒ Tc = 7.211 K

Test: Combined (Atomic + Nuclear + Solid) - Question 12

Consider a semi-empirical mass formula of the form
M = 939.6(A - Z) + 938.8Z - 14.0A + 13.0 A2/3 + 0.583Z (Z - 1) A-1/3 +19.3(A - 2Z)A-1 ±33.5A-3/4
Hence the most stable isobar is

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 12

For a most stable isobar

For A = 97, we get Z = 42.33. Hence, the most stable isobar is

Test: Combined (Atomic + Nuclear + Solid) - Question 13

Neutron lias 11011-zero magnetic moment confirm that

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 13

Since, neutron has non-zero magnetic moment. It confirm that charge distribution is not symmetric, while the total net charge of neutron is zero, but it has inner structure. It is assumed that neutron is made of quark, so it is not a fundamental particle.

Test: Combined (Atomic + Nuclear + Solid) - Question 14

According to closed-shell nucleus model parity of

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 14

Proton number is even, therefore it is all paired up, but not neutron as it is odd. Therefore, spin-parity of  is determined by the angular momentum and parity of the unpaired neutron in the1p1/2 state.
Hence, the spin parity of

Test: Combined (Atomic + Nuclear + Solid) - Question 15

41Ca has a neutron outside closed shell in f7/2. It’s nuclear magnetic momentum is equal to

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 15

The nuclear magnetic moment is given by μ = g j μN , where j is the total angular momentum.

Test: Combined (Atomic + Nuclear + Solid) - Question 16

As one moves along the line of stability from 56Fe to U235 nucleus the binding energy per nucleon decreases from 8 MeV to 7.6 MeV Tliis trend is mainly due to the

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 16

Due to short range nature of nuclear forces and long range nature of coulombic force, the binding energy per nuclear decreases fr om Fe56 to U235.

Test: Combined (Atomic + Nuclear + Solid) - Question 17

Two particles He+ and Li+ are projected in a circular orbit of same radius perpendicular to a given magnetic field

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 17

To move particle in circular motion, magnetic force provide necessaiy centripetal force.

Test: Combined (Atomic + Nuclear + Solid) - Question 18

The reaction  strong interaction is not possible because

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 18

Here, the strangeness number and isospin number are not conserved.

Test: Combined (Atomic + Nuclear + Solid) - Question 19

The life time of a free neutron to decay into a proton, an election and an anti-neutrino is approximately

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 19

Decay office neutron into a proton, election and anti-neutrino is example of weak force decay. The life ofweak decay is of about 15 minutes, i.e.. of the order 103 sec.

Test: Combined (Atomic + Nuclear + Solid) - Question 20

Consider the strong interaction process

the unknown particle X may be

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 20

Consider the reaction.

Thus the given particle with

Test: Combined (Atomic + Nuclear + Solid) - Question 21

The binding energy of the neon isotopes  is 160.65 Mev. thus, its atomic mass in atomic unit u, would be

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 21

Binding energy B = Δmc2. where Δm is mass defect

Atomic mass = A - ΔM = 20 - 0.00017 = 19.99u

Test: Combined (Atomic + Nuclear + Solid) - Question 22

Neutron can be expressed in terms of quark

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 22

Neutron particle is characterised by charge Q = 0, Baryon number B = 1 and strangeness S = 0,

Test: Combined (Atomic + Nuclear + Solid) - Question 23

There is a stream of neutrons with a speed 2.5 x 103 m/s. If half life of neutrons is 700 seconds, the fractions of neutrons that will decay before they travel a distance 10m.
(given mass of neutrons = 1.675 x 10-27kg)

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 23

Time required by the neutrons to cover distance 10 m is

Fraction ofneutrons present (undecayed) in time t

Fractions of neutron decayed = 1 -0.999952 = 0.000048
⇒ Fraction % = 0.0048%

Test: Combined (Atomic + Nuclear + Solid) - Question 24

baryon has the following properties Q = -1, S = -2 & B = 1, the quark content is

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 24

quark content of   is dss as it satisfy Q, S & B of

Test: Combined (Atomic + Nuclear + Solid) - Question 25

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 25

Test: Combined (Atomic + Nuclear + Solid) - Question 26

The quark content of ∑+, k-, π- and p is indicated

in die process π- + p → k- + ∑+
Considering strong interactions only, which of die following is true?

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 26

Test: Combined (Atomic + Nuclear + Solid) - Question 27

The conservation law violated by die reaction p  → π+ e+ is conservation of

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 27

Given reaction

Thus, above reaction is violted due to non conservation of electron lepton number and baryon number.

*Answer can only contain numeric values
Test: Combined (Atomic + Nuclear + Solid) - Question 28

The wavelength of one of the visible lines in the spectrum of the hyclrogen atom is approximately 6560 Å. It is known that this corresponds to a transition between the states with the principal quantum numbers n = 2 and n = 3. Hie frequency corresponding to the transition from die first excited state to die ground state is_______ x 1015Hz.
(Upto two decimal places)

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 28

For transition n = 2 to n = 1

*Answer can only contain numeric values
Test: Combined (Atomic + Nuclear + Solid) - Question 29

A sample of certain element is placed in a 0.3 Tesla magnetic field and suitably excited. If the wavelength corresponding to the transition 1P → 1S is 450 nm. then the separation in the Zeeman spectral lines is equal to _______ x 10-12 meter.
(Upto two decim al places)

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 29

*Answer can only contain numeric values
Test: Combined (Atomic + Nuclear + Solid) - Question 30

X-ray spectrum o f a cobalt target (Z = 27) contains strong Kα line of wavelength 0.1785 nm and a weak line having wavelength of 0.1537 nm due to an impurity. The atomic number of impurity element is_______.

Detailed Solution for Test: Combined (Atomic + Nuclear + Solid) - Question 30

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