Question Set D

TN 12th Standard Physics Recent Developments in Physics Creative Questions Study Material - QB365

Download Tamil Nadu 12th Standard Physics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

Questions:

I. choose the best answer

The speed of light in an isotropic medium depends on, ______.

(a)

its intensity

(b)

its wavelength

(c)

the nature of propagation

(d)

the motion of the source w.r.t medium

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is, ______.

(a)

2.5 cm

(b)

5cm

(c)

10 cm

(d)

15cm

An object is placed in front of a convex mirror of focal length off and the maximum and minimum distance of an object from the mirror such that the image formed is real and magnified.

(a)

2f and c

(b)

c and \(\infty\)

(c)

f and O

(d)

None of these

For light incident from air on a slab of refractive index 2, the maximum possible angle of refraction is, ______.

(a)

30^o

(b)

45^o

(c)

60^o

(d)

90^o

If the velocity and wavelength of light in air is V_a and λ_a and that in water is V_w and λ_w, then the refractive index of water is______.

(a)

\(\frac{V_W}{V_a}\)

(b)

\(\frac{V_a}{V_W}\)

(c)

\(\frac{\lambda_W}{\lambda_a}\)

(d)

\(\frac{{V_a}\lambda_a}{{V_W}\lambda_W}\)

Stars twinkle due to, ______.

(a)

reflection

(b)

total internal reflection

(c)

refraction

(d)

polarisation

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as plane sheet of glass. This implies that the liquid must have refractive index, ______.

(a)

less than one

(b)

less than that of glass

(c)

greater than that of glass

(d)

equal to that of glass

The radius of curvature of curved surface at a thin planoconvex lens is 10 cm and the refractive index is 1.5. If the plane surface is silvered, then the focal length will be, ______.

(a)

5 cm

(b)

10 cm

(c)

15 cm

(d)

20 cm

An air bubble in glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is ______.

(a)

8 cm

(b)

10 cm

(c)

12 cm

(d)

16 cm

10.

A ray of light travelling in a transparent medium of refractive index n falls, on a surface separating the medium from air at an angle of incidents of 45^o . The ray can undergo total internal reflection for the following n, ______.

(a)

n = 1.25

(b)

n = 1.33

(c)

n = 1.4

(d)

n = 1.5

11.

A plane glass is placed over a various coloured letters (violet, green, yellow, red) The letter which appears to be raised more is _____.

(a)

red

(b)

yellow

(c)

green

(d)

violet

12.

Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm approximately. The maximum distance at which these dots can be resolved by the eye is_____. [take wavelength of light, λ = 500 nm]

(a)

1 m

(b)

5 m

(c)

3 m

(d)

6 m

13.

In a Young’s double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to, _____.

(a)

(b)

\(\frac{D}{2}\)

(c)

\(\sqrt{2}\)D

(d)

\(\frac{D}{\sqrt2}\)

14.

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are _____.

(a)

5I and I

(b)

5I and 3I

(c)

9I and I

(d)

9I and 3I

15.

When light is incident on a soap film of thickness 5 x 10^–5 cm, the wavelength of light reflected maximum in the visible region is 5320 Å. Refractive index of the film will be, _____.

(a)

1.22

(b)

1.33

(c)

1.51

(d)

1.83

16.

First diffraction minimum due to a single slit of width 1.0 x 10^–5 cm is at 30^o. Then wavelength of light used is,_____.

(a)

400 \(\mathring { A } \)

(b)

500 \(\mathring { A } \)

(c)

600 \(\mathring { A } \)

(d)

700 \(\mathring { A } \)

17.

A ray of light strikes a glass plate at an angle 60^o. If the reflected and refracted rays are perpendicular to each other, the refractive index of the glass is, _____.

(a)

\(\sqrt3\)

(b)

\(\frac{3}{2}\)

(c)

\(\sqrt{\frac{3}{2}}\)

(d)

18.

One of the of Young’s double slits is covered with a glass plate as shown in figure. The position of central maximum will,_____.

(a)

get shifted downwards

(b)

get shifted upwards

(c)

will remain the same

(d)

data insufficient to conclude

19.

Light transmitted by Nicol prism is, _____.

(a)

partially polarised

(b)

unpolarised

(c)

plane polarised

(d)

elliptically polarised

20.

The transverse nature of light is shown in,

(a)

interference

(b)

diffraction

(c)

scattering

(d)

polarisation

21.

The wavelength λ_eof an electron and λ_p of a photon of same energy E are related by _____.

(a)

λ_p ∝ λ_e

(b)

\({ \lambda }_{ p }∝ \sqrt { { \lambda }_{ e } } \)

(c)

\({ \lambda }_{ p }∝ \frac { 1 }{ \sqrt { { \lambda }_{ e } } } \)

(d)

\({ \lambda }_{ p }∝ { \lambda }_{ e }^{ 2 }\)

22.

In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the voltage is changed to 224 kV, then the de Broglie wavelength associated with the electrons would _____.

(a)

increase by 2 times

(b)

decrease by 2 times

(c)

decrease by 4 times

(d)

increase by 4 times

23.

The wave associated with a moving particle of mass 3 x 10^–6 g has the same wavelength as an electron moving with a velocity 6 x 10⁶ ms^-1. The velocity of the particle is _____.

(a)

1.82 x 10^-18ms^-1

(b)

9 x 10^-2ms^-1

(c)

3 x 10^-31ms^-1

(d)

1.82 x 10^-15ms^-1

24.

When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is \(\frac{V}{4}\). The threshold wavelength for the metallic surface is _____.

(a)

4λ

(b)

5λ

(c)

\(\frac{5}{2}λ\)

(d)

3λ

25.

If a light of wavelength 330 nm is incident on a metal with work function 3.55 eV, the electrons are emitted. Then the wavelength of the wave associated with the emitted electron is _____.(Take h = 6.6 x 10^–34 Js)

(a)

< 2.75 ×10⁻⁹m

(b)

≥ 2.75 × 10⁻⁹m

(c)

≤ 2.75 × 10⁻¹²m

(d)

< 2.5 × 10⁻¹⁰m

26.

A photoelectric surface is illuminated successively by monochromatic light of wavelength λ and λ /2. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the material is _____.

(a)

\(\frac{hc}{\lambda}\)

(b)

\(\frac{2hc}{\lambda}\)

(c)

\(\frac{hc}{3\lambda}\)

(d)

\(\frac{hc}{2\lambda}\)

27.

In photoelectric emission, a radiation whose frequency is 4 times threshold frequency of a certain metal is incident on the metal. Then the maximum possible velocity of the emitted electron will be _____.

(a)

\(\sqrt { \frac { { hv }_{ o } }{ m } } \)

(b)

\(\sqrt { \frac { { 6hv }_{ o } }{ m } } \)

(c)

\(2\sqrt { \frac { { hv }_{ o } }{ m } } \)

(d)

\(\sqrt { \frac { { hv }_{ o } }{2m } } \)

28.

Two radiations with photon energies 0.9 eV and 3.3 eV respectively are falling on a metallic surface successively. If the work function of the metal is 0.6 eV, then the ratio of maximum speeds of emitted electrons in the two cases will be _____.

(a)

1:4

(b)

1:3

(c)

1:1

(d)

1:9

29.

A light source of wavelength 520 nm emits 1.04 x 10¹⁵photons per second while the second source of 460 nm produces 1.38 x 10¹⁵ photons per second. Then the ratio of power of second source to that of first source is _____.

(a)

1.00

(b)

1.02

(c)

1.5

(d)

0.98

30.

If the mean wavelength of light from sun is taken as 550 nm and its mean power as 3.8 x 10²⁶W, then the number of photons emitted per second from the sun is of the order of _____.

(a)

10⁴⁵

(b)

10⁴²

(c)

10⁵⁴

(d)

10⁵¹

31.

The threshold wavelength for a metal surface whose photoelectric work function is 3.313 eV is _____.

(a)

4125 \(\mathring { A } \)

(b)

3750\(\mathring { A } \)

(c)

6000\(\mathring { A } \)

(d)

2062.5\(\mathring { A } \)

32.

A light of wavelength 500 nm is incident on a sensitive metal plate of photoelectric work function 1.235 eV. The kinetic energy of the photoelectrons emitted is_____. (Take h = 6.6 x 10^–34Js)

(a)

0.58 eV

(b)

2.48 eV

(c)

1.24 eV

(d)

1.16 eV

33.

Photons of wavelength λ are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius R by a perpendicular magnetic field having magnitude B. The work function of the metal is _____.

(a)

\(\frac { hc }{ \lambda } -{ m }_{ e }+\frac { e^{ 2 }{ B }^{ 2 }{ R }^{ 2 } }{ { 2m }_{ e } } \)

(b)

\(\frac { hc }{ \lambda } +{ 2m }_{ e }{ \left[ \frac { eBR }{ { 2m }_{ e } } \right] }^{ 2 }\)

(c)

\(\\ \frac { hc }{ \lambda } -{ m }_{ e }{ c }^{ 2 }-\frac { e^{ 2 }{ B }^{ 2 }{ R }^{ 2 } }{ { 2m }_{ e } } \)

(d)

\(\frac { hc }{ \lambda } -{ 2m }_{ e }{ \left[ \frac { eBR }{ { 2m }_{ e } } \right] }^{ 2 }\)

34.

The work functions for metals A, B and C are 1.92 eV, 2.0 eV and 5.0 eV respectively. The metal/metals which will emit photoelectrons for a radiation of wavelength 4100 Å is/are _____.

(a)

A only

(b)

both A and B

(c)

all these metals

(d)

none

35.

Emission of electrons by the absorption of heat energy is called ______ emission.

(a)

photoelectric

(b)

field

(c)

thermionic

(d)

secondary

36.

Suppose an alpha particle accelerated by a potential of V volt is allowed to collide with a nucleus of atomic number Z, then the distance of closest approach of alpha particle to the nucleus is _____.

(a)

\(14.4\frac { Z }{ V } \mathring { A } \)

(b)

\(14.4\frac { V }{ Z } \mathring { A } \)

(c)

\(1.44\frac { Z }{ V } \mathring { A } \)

(d)

\(1.44\frac { V }{ Z } \mathring { A } \)

37.

In a hydrogen atom, the electron revolving in the fourth orbit, has angular momentum equal to _____.

(a)

(b)

\(\frac{h}{\pi}\)

(c)

\(\frac{4h}{\pi}\)

(d)

\(\frac{2h}{\pi}\)

38.

Atomic number of H-like atom with ionization potential 122.4 V for n = 1 is _____.

(a)

(b)

(c)

(d)

39.

The ratio between the radius of first three orbits of hydrogen atom is _____.

(a)

1:2:3

(b)

2:4:6

(c)

1:4:9

(d)

1:3:5

40.

The charge of cathode rays particle is _____.

(a)

Positive

(b)

negative

(c)

neutral

(d)

not defined

41.

In J.J. Thomson e/m experiment, electrons are accelerated through 2.6 kV enter the region of crossed electric field and magnetic field of strength 3.0 x 10⁴ Vm^-1 and 1.0 x 10^-3 T, respectively, and pass through it and undeflected, then the specific charge is _____.

(a)

1.6 × 10¹⁰ C kg^–1

(b)

1.7 × 10¹¹ Ckg^–1

(c)

1.5 × 10¹¹ Ckg^–1

(d)

1.8 × 10¹¹ Ckg^–1

42.

The ratio of the wavelengths radiation emitted for the transition from n = 2 to n = 1 in Li⁺⁺, He⁺and H is _____.

(a)

1:2:3

(b)

1:4:9

(c)

3:2:1

(d)

4:9:36

43.

The electric potential of an electron is given by \(V={ V }_{ 0 } \ In\left( \frac { r }{ { r }_{ 0 } } \right) \), where r₀ is a constant. If Bohr atom model is valid, then variation of radius of n^th orbit r_n with the principal quantum number n is _____.

(a)

\({ r }_{ n }∝ \frac { 1 }{ n } \)

(b)

\({ r }_{ n }∝ n\)

(c)

\({ r }_{ n }∝\frac { 1 }{ { n }^{ 2 } } \)

(d)

\({ r }_{ n }∝ { n }^{ 2 }\)

44.

If the nuclear radius of ²⁷Al is 3.6 fermi, the approximate nuclear radius of ⁶⁴Cu, in femi is _____.

(a)

2:4

(b)

1.2

(c)

4.8

(d)

3.6

45.

The nucleus is approximately spherical in shape. Then the surface area of nucleus having mass number A varies as _____.

(a)

A^2/3

(b)

A^4/3

(c)

A^1/3

(d)

A^5/3

46.

The mass of a ₃⁷Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of ₃⁷Li nucleus is nearly _____.

(a)

46 MeV

(b)

5.6 MeV

(c)

3.9 MeV

(d)

23 MeV

47.

M_p denotes the mass of the proton and M_n denotes mass of a neutron. A given nucleus of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by _____.(where c is the speed of light)

(a)

M (N,Z) = NM_n+ ZM_p- Bc²

(b)

M (N,Z) = NM_n+ ZM_p+ Bc²

(c)

M (N,Z) = NM_n+ ZM_p- B/c²

(d)

M (N,Z) = NM_n+ ZM_p+ B/c²

48.

A radioactive nucleus (initial mass number A and atomic number Z) emits two α-particles and 2 positons. The ratio of number of neutrons to that of proton in the final nucleus will be _____.

(a)

\(\frac{A-Z-4}{Z-2}\)

(b)

\(\frac{A-Z-2}{Z-6}\)

(c)

\(\frac{A-Z-4}{Z-6}\)

(d)

\(\frac{A-Z-12}{Z-4}\)

49.

The half-life period of a radioactive element A is same as the mean life time of another radioactive element B. Initially both have the same number of atoms. Then _____.

(a)

A and B have the same decay rate initially

(b)

A and B decay at the same rate always

(c)

B will decay at faster rate than A

(d)

A will decay at faster rate than B

50.

A radiative element has N₀ number of nuclei at t = 0. The number of nuclei remaining after half of a half-life _____.(that is, at time t = \(\frac{1}{2}T_\frac{1}{2}\))

(a)

\(\frac{N_0}{2}\)

(b)

\(\frac{N_0}{\sqrt2}\)

(c)

\(\frac{N_0}{4}\)

(d)

\(\frac{N_0}{8}\)

51.

The barrier potential of a silicon diode is approximately, ______.

(a)

0.7 V

(b)

0.3 V

(c)

2.0 V

(d)

2.2 V

52.

If a small amount of antimony (Sb) is added to germanium crystal,______.

(a)

it becomes a p-type semiconductor

(b)

the antimony becomes an acceptor atom

(c)

there will be more free electrons than hole in the semiconductor

(d)

its resistance is increased

53.

If a positive half-wave rectified voltage is fed to a load resistor, for which part of a cycle there will be current flow through the load?

(a)

0⁰–90⁰

(b)

90⁰–180⁰

(c)

0⁰–180⁰

(d)

0⁰–360⁰

54.

The zener diode is primarily used as ______.

(a)

Rectifier

(b)

Amplifier

(c)

Oscillator

(d)

Voltage regulator

55.

The principle based on which a solar cell operates is______.

(a)

Diffusion

(b)

Recombination

(c)

Photovoltaic action

(d)

Carrier flow

56.

The light emitted in an LED is due to ______.

(a)

Recombination of charge carriers

(b)

Reflection of light due to lens action

(c)

Amplification of light falling at the junction

(d)

Large current capacity

57.

To obtain sustained oscillation in an oscillator,______.

(a)

Feedback should be positive

(b)

Feedback factor must be unity

(c)

Phase shift must be 0 or 2π

(d)

All the above

58.

If the input to the NOT gate is A = 1011, its output is ______.

(a)

0100

(b)

1000

(c)

1100

(d)

0011

59.

Which one of the following represents forward bias diode?

(a)

(b)

(c)

(d)

60.

The given electrical network is equivalent to ______.

(a)

AND gate

(b)

OR gate

(c)

NOR gate

(d)

NOT gate

61.

The output of the following circuit is 1 when the input ABC is______.

(a)

101

(b)

100

(c)

110

(d)

010

62.

The variation of frequency of carrier wave with respect to the amplitude of the modulating signal is called ______.

(a)

Amplitude modulation

(b)

Frequency modulation

(c)

Phase modulation

(d)

Pulse width modulation

63.

The frequency range of 3 MHz to 30 MHz is used for ______.

(a)

Ground wave propagation

(b)

Space wave propagation

(c)

Sky wave propagation

(d)

Satellite communication

64.

The particle size of ZnO material is 30 nm. Based on the dimension it is classified as _____.

(a)

Bulk material

(b)

Nanomaterial

(c)

Soft material

(d)

Magnetic material

65.

Which one of the following is the natural nanomaterial.

(a)

Peacock feather

(b)

Peacock beak

(c)

Grain of sand

(d)

Skin of the Whale

66.

The blue print for making ultra durable synthetic material is mimicked from _____.

(a)

Lotus leaf

(b)

Morpho butterfly

(c)

Parrot fish

(d)

Peacock feather

67.

The method of making nanomaterial by assembling the atoms is called _____.

(a)

Top down approach

(b)

Bottom up approach

(c)

Cross down approach

(d)

Diagonal approach

68.

“Sky wax” is an application of nano product in the field of _____.

(a)

Medicine

(b)

Textile

(c)

Sports

(d)

Automotive industry

69.

The materials used in Robotics are _____.

(a)

Aluminium and silver

(b)

Silver and gold

(c)

Copper and gold

(d)

Steel and aluminum

70.

The alloys used for muscle wires in Robots are _____.

(a)

Shape memory alloys

(b)

Gold copper alloys

(c)

Gold silver alloys

(d)

Two dimensional alloys

71.

The technology used for stopping the brain from processing pain is _____.

(a)

Precision medicine

(b)

Wireless brain sensor

(c)

Virtual reality

(d)

Radiology

72.

The particle which gives mass to protons and neutrons are _____.

(a)

Higgs particle

(b)

Einstein particle

(c)

Nanoparticle

(d)

Bulk particle

73.

The gravitational waves were theoretically proposed by _____.

(a)

Conrad Rontgen

(b)

Marie Curie

(c)

Albert Einstein

(d)

Edward Purcell

74.

The barrier potential of a p-n junction depends on
i) type of semiconductor material
ii) amount of doping
iii) temperature. Which one of the following is correct?

(a)

(i) and (ii) only

(b)

(ii) only

(c)

(ii) and (iii) only

(d)

(i) (ii) and (iii)

75.

In an unbiased p-n junction, the majority charge carriers (that is, holes) in the p-region diffuse into n-region because of ______.

(a)

the potential difference across the p-n junction

(b)

the higher hole concentration in p-region than that in n-region

(c)

the attraction of free electrons of n-region

(d)

the higher concentration of electrons in the n-region than that in the p-region

Visit QB365-SLMS - https://www.qb365.in/slms/

Answers Key:

I. choose the best answer

v = nג
In an isotropic medium, there is no change in the frequency of the light. So, the speed of light depends on wavelength of light.

At end A,
\(\frac{1}{f} =\frac{1}{u_A}+\frac{1}{v_A} \)
\(\therefore \frac{1}{v_A} =\frac{1}{-10}-\frac{1}{-20} \)
\(\frac{1}{v_A} =-\frac{1}{10}+\frac{1}{20}=\frac{-2+1}{20}=-\frac{1}{20} \)
\(v_A =-20 \mathrm{~cm} \)
\(\left|v_{\wedge}\right|=20 \mathrm{~cm}\)
At end B,
\(\frac{1}{f} =\frac{1}{u_B}+\frac{1}{v_B} \)
\(\frac{1}{v_B} =\frac{1}{f}-\frac{1}{u_B}, \)
\(u_B =-30 \mathrm{~cm} \)
\(\frac{1}{v_B} =-\frac{1}{10}+\frac{1}{30} \)
\(=\frac{-3+1}{30}=\frac{-2}{30}=\frac{-1}{15} \)
\(v_B =-15 \mathrm{~cm} \)
\(\left|v_B\right| =15 \mathrm{~cm} \)
\(\therefore \quad\left|\mathrm{v}_{\mathrm{A}}\right|-\left|\mathrm{v}_{\mathrm{B}}\right| \) is the length of the image
= 20 - 15 = 5 cm

Convex Mirror is diverging in nature and for all positions of objects, convex mirror forms virtual and erect image.

(a)
30^o

Refractive index of water \(=\frac{Velocity \ of \ light \ in \ air(V_s)}{Velocity \ of \ light \ in \ water(V_w)}\)

\(\frac{I}{f}=\left(\frac{\mu_{\mathrm{L}}}{\mu_L}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\)
When the biconvex lens of glass dipped in liquid, it acts as a plane sheet of glass.
\(\therefore \mathrm{f}=\infty, \frac{1}{\mathrm{f}}=0 \quad \frac{\mu_g}{\mu_{\mathrm{L}}}-1=0 ; \frac{\mu_{\mathrm{s}}}{\mu_{\mathrm{L}}}=1, \mu_{\mathrm{s}}=\mu_{\mathrm{L}}\)

\(\frac{1}{f} =(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \)
\(=(1.5-1)\left(\frac{1}{\infty}-\frac{1}{(-10)}\right)\)
(Since plano convex lens)
\(=0.5\left[\frac{1}{10}\right]=\frac{1}{20} \)
\(\mathrm{f}_t =20 \mathrm{~cm}\)
Formula for silvered lenses
\(\frac{1}{\mathrm{~F}} =\frac{2}{\mathrm{f}_1}+\frac{1}{\mathrm{f}_m} \)
\(\frac{1}{\mathrm{~F}} =\frac{2}{20}+\frac{1}{\infty} \)
\(\therefore \mathrm{F} =\frac{20}{2}=10 \mathrm{~cm}\)

Apparent depth = 3 + 5 = 8 cm
Real depth = thickness of the slab = t
n = 1.5
\(n=\frac{Real \ depth}{Apparent \ depth}\)
\(\therefore 1.5=\frac{t}{8}\)
t = 1.5 x 8
t = 12 cm

10.

For total internal reflection,
sin i > sin c
\(n=\frac{1}{sin \ c}\)
\(sin \ c=\frac{1}{n}\)
\(sin \ i>\frac{1}{n}\)
\(n>\frac{1}{sin \ i}\)
n >\(\sqrt{2}\)
n >1.414 = 1.5

11.

Refractive index for violet is more and wavelength for violet is very low comparing other colours. So, the letter which appears to be raised more is violet.

12.

λ = 500 nm = 500 x 10^-9 m
x = 3 mm = 3 x 10^-3 m
a = 1 mm = 1 x 10^-3 m
\(d=\frac{xa}{1.22 \lambda}\)
\(d=\frac{3 \times1\times10^{-6}}{1.22 \times500\times10^{-9}}\)
\(=\frac{3 \times1\times10^{-6}}{6.10 \times 10^{-7}}\)
\(d=\frac{30}{6.1}=5 m\)

13.

d' = 2d, β' = β, D' = ?
W.K.T, Fringe width
\(\beta = \frac{D\lambda}{d} \Rightarrow D' = \frac{Dd'}{d}\)
\(D' = \frac{D2d}{d}=2D\)

14.

I = l₁ + l₂ + 2\(\sqrt{I_1I_2}\)cos θ
If cos θ = cos 0 = l, I is max
= I+ 4I + 2\(\sqrt{41^2}\) cos 0
= 5I + 4I = 91
If cos π = -1, I is min
I_min = I + 4I + 2\(\sqrt{41^2}\) cos π
= 5I + 4I(-1)
= 5I + 4I = I
(I_max, I_min)= (9I, I)

15.

2n t cos r = (2m + 1) \(\frac{\lambda}{2}\)
For maximum
m = 2 (For visible region), n - refractive index.
cos r = cos 0 = 1
t = 5 x 10^-5 x 10^-2 = 5 x 10^-7 m
\(n=\frac{(2m+1)\frac{\lambda}{2}}{2t}=\frac{5\lambda}{2 \times 2 \times t}\)
\(=\frac{5 \times5320\times10^{-10}}{4 \times 5 \times 10^{-7}}\)
\(=\frac{5 \times5320\times10^{-10}}{20}=1330 \times 10^3\)
n = 1.330

16.

(b)
500 \(\mathring { A } \)

17.

n = tan i_p = tan 60^o = \(\sqrt{3}\)

18.

(b)
get shifted upwards

19.

20.

(d)
polarisation

21.

\(\mathrm{E}_{\mathrm{p}} =\frac{\mathrm{hc}}{\lambda_{\mathrm{p}}} \)
\(\mathrm{E}_{\mathrm{e}} =\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda_{\mathrm{e}}^2} \)
\(\frac{\mathrm{hc}}{\lambda_{\mathrm{p}}} =\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda_{\mathrm{e}}^2} \)
\(\lambda_{\mathrm{p}} \propto \lambda_{\mathrm{e}}^{{ }^2}\)

22.

\(\lambda\propto \frac{1}{\sqrt{V}}\)
\(\frac{\lambda_1}{\lambda_2}=\frac{\sqrt{224\times10^3}}{\sqrt{14\times 10^3}}\)
\(=\sqrt{16}=4\)
\(\lambda_{\mathrm{2}}= \frac{\lambda_1}{4}\)

23.

\(\lambda_{\mathrm{i}} \frac{1}{\mathrm{mv}} \)
\(\frac{\lambda_p}{\lambda_e} =\frac{m_e v_e}{m_P v_P} \)
\(1 =\frac{9.1 \times 10^{-31} \times 6 \times 10^6}{3 \times 10^{-9} \times v_p} \)
\(\mathrm{v}_{\mathrm{p}} =9.1 \times 10^{-16} \times 2 \)
\(\mathrm{v}_{\mathrm{p}} =18.2 \times 10^{-16} \)
\(\mathrm{v}_{\mathrm{p}} =1.82 \times 10^{-15} \mathrm{~m} \mathrm{~s}^{-1}\)

24.

\(\frac{\mathrm{hc}}{\lambda}=\phi+\mathrm{eV} \) .....(1)
\(\frac{\mathrm{hc}}{2 \lambda}=\phi+\frac{\mathrm{eV}}{4}\) .....(2)
multiply (2) eqn by 4
\(\frac{2 h c}{\lambda}=4 \phi+\mathrm{eV}\) .....(3)
subtract eqn (1) from (3), we get
\(\frac{ h c}{\lambda}=3 \phi \Rightarrow \phi = \frac{ h c}{3\lambda}\)
\(\frac{ h c}{\lambda_o}=\frac{ h c}{3\lambda}\)
⋋_o = 3⋋

25.

(b)
≥ 2.75 × 10⁻⁹m

26.

\(\frac{\mathrm{hc}}{\lambda} =\phi+\mathrm{K} . \mathrm{E} .....(1) \)
\(\frac{2 \mathrm{hc}}{\lambda} =\phi+3 \mathrm{~K} . \mathrm{E}......(2)\)
multiply eqn. (1) by 3, we get
\(\frac{3 \mathrm{hc}}{\lambda} =3\phi+3 \mathrm{~K} . \mathrm{E} .....(3)\)
Subtract eqn. (2) from (3), we get
\(\frac{\mathrm{hc}}{\lambda} =2\phi \)
\(\phi=\frac{ \mathrm{hc}}{2\lambda} \)

27.

(b)
\(\sqrt { \frac { { 6hv }_{ o } }{ m } } \)

28.

K.E= hv - Φ
K.E₁ = 0.9 - 0.6 = 0.3 eV
K.E₂ = 3.3 - 0.6 = 2.7 ev
K.E ∝ v²
\(\frac{0.3}{2.7}=\frac{v^2_1}{v^2_2} \)
\(\frac{v^1}{v^2} =\frac{1}{3}\)

29.

\(P =\frac{E}{t}=\frac{n h v}{t}=\frac{n h c}{\lambda t} \Rightarrow P \propto n / t \)
\(\frac{P_1}{P_2} =\frac{1.38 \times 10^{15}}{460} \times \frac{520}{1.04 \times 10^{15}}=1.5\)

30.

\(\mathrm{P} =\frac{\mathrm{n}}{\mathrm{t}} \frac{\mathrm{hc}}{\lambda} \)
\(\frac{\mathrm{n}}{\mathrm{t}} =\frac{\mathrm{P} \lambda}{\mathrm{hc}} \)
\(\frac{\mathrm{n}}{\mathrm{t}} =\frac{3.8 \times 10^{26} \times 550 \times 10^{-9}}{6.6 \times 10^{-3} \times 3 \times 10^8}=1 \times 10^{-15}\)

31.

\(\lambda_0 =\frac{h c}{\phi} \)
\(=\frac{6.626 \times 10^{-34} \times 3 \times 10^8}{3.313 \times 1.6 \times 10^{-19}} \)
\( =\frac{19.8782400}{5.3} \times 10^{-7} \)
\(\lambda_0 =3.750 \times 10^{-7} \simeq 3750 \stackrel{o}A\)

32.

\(K .E_{\max } =\mathrm{hv}-\phi \)
\(=\frac{\mathrm{hc}}{\lambda}-\phi \)
\(\mathrm{E} =\frac{6.6 \times 10^{-34} \times 3 \times 10^8-1.235}{500 \times 10^{-9} \times 1.6 \times 10^{-19}} \)
\(=2.475-1.235 \)
\(\text {K. } \mathrm{E}_{\max } =1.24 \mathrm{eV}\)

33.

\(\text {K.E } =\frac{B^2 q^2 r^2}{2 m} \)
\(\phi =\frac{h c}{\lambda}-K . E \)
\(=\frac{h c}{\lambda}-\frac{B^2 q^2 r^2}{2 m} \)
\(\phi =\frac{h c}{\lambda}-2 m\left(\frac{B q r}{2 m}\right)^2\)

34.

\(E=\frac{12400 \stackrel{o}A}{4100 \stackrel{o}A}=3.02 eV\)

35.

36.

(b)
\(14.4\frac { V }{ Z } \mathring { A } \)

37.

\(L=\frac{nh}{2\pi}=\frac{4h}{2\pi}=\frac{2h}{\pi}\)

38.

\(V_{ionisation}=\frac{13.6}{n^2}Z^2 volt\)
\(Z=\sqrt\frac{V\times n^2}{13.6}=\sqrt\frac{122.4 \times I^2}{13.6}=\sqrt{9}=3\)

39.

r_n ∞ n²
r₁: r₂: r₃ = 1: 4: 9

40.

Cathode rays are stream of negatively charged electron.

41.

(b)
1.7 × 10¹¹ Ckg^–1

42.

\(\frac{1}{\lambda}=\mathrm{RZ}^2\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right] \)
\(\frac{1}{\lambda}=\mathrm{RZ} ^2\left[\frac{1}{1}-\frac{1}{4}\right]=\frac{3}{4} \mathrm{RZ}^2 \)
\(\lambda \propto \frac{1}{Z^2} \)
\(\lambda_{\mathrm{Li}}: \lambda_{\mathrm{H} c}: \lambda_{\mathrm{H}}=\frac{1}{9}: \frac{1}{4}: \frac{1}{1}=4: 9: 36\)

43.

Electric potential in n^th orbit
\(\mathrm{V} =\mathrm{V}_0 \ln \left(\frac{\mathrm{r}_{\mathrm{n}}}{\mathrm{r}_0}\right) \)
\(=\mathrm{V}_0\left(\ln \mathrm{r}_{\mathrm{n}}-\ln \mathrm{r}_0\right) \)
\(=\mathrm{V}_0 \ln \mathrm{r}_{\mathrm{n}}-\mathrm{V}_0 \ln \mathrm{r}_0\)
\(\left|\mathrm{F}_\epsilon\right|=\mathrm{e} \frac{\mathrm{dv}}{\mathrm{dr}} =\mathrm{e} \frac{\mathrm{d}}{\mathrm{dr}}\left(\mathrm{V}_b / n \mathrm{r}_B-\mathrm{V}_0 / m \mathrm{r}_0\right) \)
\(=\mathrm{c}\left(\frac{\mathrm{V}_0}{\mathrm{r}_n}-0\right)=\frac{\mathrm{eV}}{\mathrm{r}_{\mathrm{n}}} \)
Centripetal force = coulomb force
\(\frac{m v^2}{r_n}=\mathrm{c} \frac{V_0}{r_n} \Rightarrow v=\sqrt{\frac{e V_0}{m}}=\text { constant }\)
Angular momentum,
\(\mathrm{mvr}_n=\frac{\mathrm{nh}}{2 \pi}\)
\(\mathrm{m}, \mathrm{v}, \mathrm{h}, 2 \pi\) are constants
hence, r_n ∝ n

44.

\(r \propto A^{\frac{1}{3}} \)
\(\frac{r_{\mathrm{Cu}}}{\mathrm{r}_{\mathrm{Al}}}=\frac{\mathrm{A}_{\mathrm{Cu}}^\frac{1}{3}}{\mathrm{~A}_{\mathrm{Al}}^{\frac{1}{3}}}=\frac{4}{3} \)
\(\mathrm{r}_{\mathrm{Cu}}=\frac{4}{3} \times 3.6 \mathrm{~F}=4.8 \mathrm{~F}\)

45.

r ∝ A^1/3
Surface Area = 4πr²
Hence, Surface Area ∝ A^2/3

46.

\(\frac{BE}{A}=\frac{\Delta\times931MeV}{V}=\frac{0.042 \times931}{7}\)
= 5.586 = 5.6 MeV

47.

B = ∆m x c²
∆m = \(\frac{B}{c^2}\)
N M_n + Z M_p - M(N,Z) = \(\frac{B}{c^2}\)
N (N,Z) = N M_n + ZM_p - \(\frac{B}{c^2}\)

48.

^A_ZX = 2⁴₂He + 2⁰₁e + ^A_ⁱ2iY
\(\frac{N_i}{Z_i}=\frac{(A_i-Z_i)}{Z_i} =\frac{A-8-(Z-6)}{Z-6}=\frac{A-Z-2}{Z-6}\)

49.

T_A1/2 = ፒ_B
\(\frac{0.6931}{\lambda_{\mathrm{A}}}=\frac{1}{\lambda_{\mathrm{B}}} \)
\(\lambda_{\mathrm{B}}=\frac{\lambda_{\mathrm{A}}}{0.6931}=1.44 \lambda_{\mathrm{A}}\)
Hence, B will decay at faster rate than A

50.

(b)
\(\frac{N_0}{\sqrt2}\)

51.

(a)
0.7 V

52.

53.

54.

(d)
Voltage regulator

55.

56.

(a)
Recombination of charge carriers

57.

(d)
All the above

58.

\(y=\overline{A}=\overline{1011}=0100\)
The Boolean expression for NOT gate, \(y=\bar{A}\)

59.

60.

\(Y_1=\overline{A+B}, y_2=\overline{A+B}=A+B, y=\overline{A+B}\)

61.

A = 1, B = 0, C = 1
y = A + B, y = (A + B).C
y = (1 + 0).1 ⇒ y = 1

62.

(b)
Frequency modulation

63.

Ground wave propagation: frequency less than 2 MHz
Sky wave propagation: 3 to 30 MHz
Space wave propagation: Above 30 MHz to 400 GHz
Satellite communication: uplink communication 6 GHz band downlink communication 4 GHz band

64.

Size of the particle is between
1-100 nm - Nano.
Size of the particle is greater
than-100 nm - Bulk.

65.

Wings of a morpho butterfly, peacock feathers, lotus leaf surface and sources of parrot fish's bite are some of the natural nano particles.

66.

Parrot fish's source of bite → mimic → Ultra durable synthetic material.
Lotus leaf surface → SEM → Self Cleaning Process
The scales on the wings of a morpho butterfly → mimic → Interaction of colours.
Peacock feathers → mimic → Glowing in different colours.

67.

There are two type of Synthesis of nano materials:
(i) Bottom up - Assembling atoms together.
(ii) Top down Breaking down bulk solid.

68.

69.

(d)
Steel and aluminum

70.

They are thin strands of wire made of shape memory alloys. They can contract by 5% when electric current is passed through them.

71.

Medical virtual reality is effectively used to stop the brain from processing pain and cure soreness.

72.

Proton and neutron are made up of quarks. Later, it was found that Higg's particles or God particles give mass to the particles like protons, neutrons etc.

73.

Albert Einstein theoretically proposed the existence of gravitational waves in the year 1915.

74.