Class 12th

In a semiconductor, the number density of intrinsic charge carriers at 27°C is 1.5 * 10¹? / m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5*10²² / m³. The electron density in the doped semiconductor is __________ x 10? / m³.

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Contributor-Level 10

ni² = ne * nh
(1.5*10¹? )² = ne * (4.5*10²²)
ne = (2.25 * 10³²)/ (4.5 * 10²²) = 0.5 * 10¹? = 5 * 10? / m³

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4 months ago

A system consists of two types of gas molecules A and B having same number density 2*10²⁵ / m³. The diameter of A and B are 10 Å and 5 Å respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is __________ x10⁻².

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Contributor-Level 10

Mean free path:
λ ∝ 1/ (nd²)
λA/λB = (d_B²/d_A²) = (5²/10²) = 25/100 = 25 * 10? ²

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4 months ago

A message single of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 volt. The modulation index will be __________.

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Class 12th Dual Nature of Radiation and Matter

Contributor-Level 10

Modulation Index
μ = Am/Ac = 20/20 = 1

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4 months ago

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30cm. The value of B is __________ x x 10⁻⁷ T
Given hc = 20 * 10?²? J-m, mass of electron = 9 * 10⁻³¹ kg

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Contributor-Level 10

K = hc/λ - W?
K = (20*10? ²? )/ (500*10? ) - 1.25 * 1.6*10? ¹?
K = 4*10? ¹? - 2*10? ¹? = 2*10? ¹? J
R = √ (2mK)/ (eB)
B = √ (2mK)/ (eR) = √ (2 * 9*10? ³¹ * 2*10? ¹? ) / (1.6*10? ¹? * 30*10? ²)
B = √ (36*10? ) / (48*10? ²¹) = (6*10? ²? ) / (4.8*10? ²? ) = 1.25 * 10? T
B = 125 * 10? T

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4 months ago

Two circuits are shown in the figure (a) & (b). At a frequency of __________ rad /s the average power dissipated in one cycle will be same in both the circuits.

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Contributor-Level 10

Power dissipated is same
P? = P?
P_R = P_RLC
(V²/R) = (V²/Z)cos (φ) = (V²/Z) (R/Z) = V²R/Z²
R = R²/Z² => Z² = R²
R² + (ωL - 1/ωC)² = R²
ωL = 1/ωC
ω = 1/√ (LC) = 1/√ (0.1 * 40 * 10? ) = 1/√ (4 * 10? ) = 1/ (2 * 10? ³) = 500 rad/s

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4 months ago

A radioactive sample has an average life of 30ms and is decaying. A capacitor of capacitance 200 µF is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _______ Ω.

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Contributor-Level 10

= 1/λ = 30*10? ³ sec.
C = 200µF, R
Q/A = constant [Given]
A = A? e? & Q = Q? e? /?
Q/A = (Q? /A? ) e^ (-t/RC + λt) = constant
For this to be constant, the exponent must be zero.
-t/RC + λt = 0
1/RC = λ
R = 1/ (λC) = /C = 30*10? ³/200*10? = 150 Ω

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4 months ago

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Å. If the speed of electron is 2.2 * 10? m/s, then the current associated with the electron will be _______ * 10?² mA. [Take π as 22/7]

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Class 12th Magnetism and Matter

Contributor-Level 10

r = 0.5Å = 0.5*10? ¹? m
v = 2.2*10? m/s
I =?
t = 2πr/v
I = e/t = ev/2πr = (1.6*10? ¹? * 2.2*10? )/ (2 * 22/7 * 0.5*10? ¹? )
I ≈ 1.12*10? ³ A = 1.12 mA = 112 * 10? ² mA

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4 months ago

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 * 10?² A/m² and moment of inertia 5 * 10? kg m². If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _______ mT. [Take π² as 9.85]

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Class 12th Communication Systems

Contributor-Level 10

M = 9.85*10? ² A/m²

I = 5*10? kg-m²

T = 5s/10osc = 0.5 sec

B =?

T = 2π√ (I/MB)

B = 4π²I/ (MT²) = (4*9.85*5*10? )/ (9.85*10? ² * 0.5²)

B = (20*10? )/ (10? ² * 0.25) = 800*10? = 0.8*10? ³ T = 8mT

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4 months ago

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulate by a 7.7 kHz sine wave of 5 V amplitude are (a/10) V and ( b/10 ) V respectively. Then the value of a/b is _______.

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Class 12th Dual Nature of Radiation and Matter

Contributor-Level 10

Amplitude of sidebands = µAc/2
Here µ = Am/Ac = 5/15 = 1/3
Amplitude = (1/3) (15)/2 = 2.5 V
a/10 = 2.5 => a = 25
b/10 = 2.5 => b = 25
a/b = 1

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4 months ago

A particle of mass 9.1 * 10?³¹ kg travels in a medium with a speed of 10? m/s and a photon of a radiation of linear momentum 10?²? kg m/s travels in vacuum. The wavelength of photon is _______ times the wavelength of the particle.

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