A beam of protons enters a uniform magnetic field of 0.3 Tesla with a velocity of 4 x 10⁵ m/sec at an angle of 60° to the field. The radius of the helical path taken by the beam is
v1 is responsible for horizontal motion of proton
v2 is responsible for circular motion of proton
Mass of proton = 1.67 * 10-27 Kg
Charge on proton= 1.6 * 10-19 C
∴ mv22 / r = qv2 B
r = mv2 /qB
= 1.67 * 10-27 * 4 x 10⁵ / 1.6 * 10-19 * 0.3
= 0.013 m
Pitch of helix = v1 x T
Where T = 2πr / v2
= 2πr / v sin θ
⇒ Pitch of helix = v cos θ x 2πr / v sin θ
= 2 πr cotθ
= 2x 3.14 x 0.013 x cot 60°
= 0.0471 m
= 47.1 mm
The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is __________
A particle travelling along the positive X- axis with energy E incident on a potential barrier (Vo), which of the following represent the correct wave- form for Vo > E ?
A parallel beam of light travelling in water (refractive index = 4/3) is refracted by a spherical air bubble of radius 2mm situated in water. Assuming the light rays to be parallel, find the position of the final image ?
Which of the following matrices is hermitian ?
The normalized wave function of the hydrogen atom for 1st state is where being the Bohr radius. The expectation value of potential energy in this state is __
An AC source producing emf is connected in series with a capacitor and a resistor. The steady- state current in the circuit is found to be Which of the following depicts the correct relation?
A neutron moving with speed V makes a head on collision with a hydrogen atom in ground state kept at rest find the minimum kinetic energy of the neutron for which inelastic collision may take place if neutron and hydrogen atom travel with velocity V1 and V2 respectively after collision?
The correct curve between intensity of magnetisation (I) and magnetic field (H) for a ferromagnetic substance is given by.
The group velocity of electromagnetic waves moving with phase velocity c in a dispersive medium of refractive index n is given by :
The radii of Cs and Cl are r1 and r2 respectively the lattice constant if it crystallizes in bcc structure is :
The momentum of an electron (mass m) which has the same kinetic energy as its rest mass energy is:
If at t = 0 the particle is in state where re the ground and first excited states, respectively for a particle in a cubical box of size a, the state vector ψ(x, t), for t > 0 in the Schrodinger picture is:
then the average value of the position vector in the range – L/2 to + L/2 is given by
The electric field of a wave propagating in the x – y plane, with wave vector k→
making an angleof 30o with the x- axis is:
The correct plot for the equivalent one dimensional potential for an attractive inverse fourth law of force :
The Lorentz transformation are equivalent to rotation of axes in four dimensional space through an imaginary angle ______
The transistor gain of the circuit shown in the figure is given by ______
The total energy of an ionic solid is given by where a is the Madelung constant, r is the distance between the nearest neighbour in the crystal. If r0 is the equilibrium separation then the constant B is given by ______
In a simple cubic lattice d100 : d110 : d111 is _____
Order and degree of the differential equation
For an n- p- n transistor connected as shown in the figure. VBE = 0.7V. Given that reverse saturation current of the junction at room temperature 300o k is 10-13 A, the emitter current is ______
A two dimensional lattice has that basic vectors The basic vectors of the reciprocal lattice will be ____
XY is an infinite line charge distribution. P and Q are points as shown. The ratio of electric field at P and Q is :
A system consists of three spin half particles the Z- component of whose spin SZ(1), SZ(2) and SZ(3) can take any value +1/2 and - 1/2. The total spin of the system is SZ = SZ (1) + SZ (2) + SZ (3). The total number of possible micro states for this system is _______
The output voltage of a certain op- amp appears as shown in figure in response to a step input,
The slew rate is :
The figure shown in the energy level diagram corresponds to a
If we introduce the operators
Then which relation is correct:-
Which of the following expressions is in the sum-of-products (SOP) form?
What are the Eigen values of given matrix ?
The independent solution of the equations :
Two ideal batteried of emf V1 and V2 and three resistanced R1, R2 and R3 are connected as shown in the figure. The current in resistance R1 would be zero if
Which of these points are correct for stationary waves :
Which of the following class of particles obey Pauli’s exclusion principle ?
A body with charge q starts from rest and acquire a velocity n = 0.5 c. Then the new charge in it is/are :
A particle of mass ‘m’ moves in a unidimensional potential field Which is (are) correct option :
An identical collection of N two level systems is in thermal equilibrium at temperature T. Each System has a ground state energy –E and on excited state energy E.
What is (are) correct option for this state :
If the operator is Hermition, then calculate the probability of finding the particle (Which satisfies Aˆ ψ( x ) = 0 ) in the region 1 £ x £ 1.
Determine the output voltage of an op- amp for input voltages of Vi1 = 150 µV, Vi2 = 140 µV. The amplifier has differential gain of A2 = 4000 and value of CMRR is 100. (Answer in mV).
In a material two energy have a wavelength separation of 1 µm. What would be the effective temperature when the upper level is twice as densely populated as the lower level ?
Calculate the volume of the surface integral where s is the surface the sphere x2 + y2 + z2 = 4 and nÆ is the unit outward normal to the sphere and
A certain gas obeys the equation of state PV = RT + bP.
Calculate ΔU, Q and W, when 1 mole of the gas expands reversibly at 300 K from 0.220 to 20.02 for isothermal case ?
The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lα x- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?
Find the directional derivative of the point (2, 0, 3) is the direction of the outward normal to the sphere x2 + y2 + z2 = 14 at the points (3, 4, 0) ?
Determine the d.c. bias voltage VCE and the current IC for the voltage divider configuration as given in the figure.
Calculate the free electron energy of which the first Bragg reflection occurs in 1- Dimensional crystal with atomic spacing 2.5 Å. (where v atomic space is 5 Å) (give the answer in eV).
If the intergal is independent of path of joining the points (1, 2) and (3, 4). Hence evaluate the integral.
What must be the thickness of the base of a flint glass prism which resolve the sodium D- lines. the refraction index of the galss prism change w.r.t. wavelength by magnitude of – 952 cm–1 ?
At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.
Let r be the distance of the given point from the centre of the earth. Then,
Gravitational potential = -GM/r = -5.12 × 107 J/kg ...... (1)
and acceleration due to gravity,g = GM/r2 = 6.4 m/s2 ...... (2)
Dividing (1) by (2), we get
r = 5.12 x 107 / 6.4 = 8 × 106 m = 8000km
Thus, height of the point from earth's surface = r - R = 8000 - 6400 = 1600 km
A system of two particle is distributed among three single states. In how many ways can the particles be distributed if they obey Bose- Einstein statistics ?
A particle moves in a circular orbit about the origin under the action of a central If the
potential energy is zero at ∞, then the total energy of particle is _______.
If a 3- Dimensional quantum mechanical Harmonic oscillator has an energy 3.5h w in a particular state then the degree of degeneracy is _________
Determine V0 for the circuit with the input waveform as shown with VT = 0.7 V.
What is the numerical value of
The force of a 3 × 3 matrix is 2. Two of its eigen value are 1 and 2. The third eigen value is ______.
At the time t = 0, the wave function for Hydrogen atom is
A condenser of 250 µF is connected in parallel to a coil of inductance 0.16 mH and effective resistance 20 W. The resonant frequency will be ______ (give Answer in KHz)
The binding energy per nucleon is maximum for the nucleus:
Excluding the lighter nuclei, the average binding energy per nucleon is about 8 MeV. The maximum binding energy per nucleon occurs at around mass number A = 50, and corresponds to the most stable nuclei. Iron nucleus Fe56 is located close to the peak with a binding energy per nucleon value of approximately 8.8 MeV.