In the hydrogen atom spectrum, the ratio of the energy for the transition n = 3 → n = 1 to that of n = 4 —>n = 1 is
The ^{32}P radio isotope used in leukemia theraphy has t_{1/2} = 14.26 days, what % of ^{32}P remains after 35 days
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The wave function ψ of a quantum mechanical system described by a Hamiltonian can be written as a linear combination of φ_{1}and φ_{2} which are the eigen functions of H with eigen values E_{1} and E_{2} respectively . At t = 0, the system is prepared in the state
and then allowed to evolve with time. The wave function at time t = will be
An engine absorb heat at a temperature of 1000 K and rejects heat at 600 K. If the engine operates at maximum possible efficiency, the amount of work performed by the engine for 2000 J heat input is
One mole of a perfect gas is heated at a constant pressure of 1 atm from 0°C to 100°C. What is the change in internal energy?
For an assembly of molecules (molar mas = M) at temperature T, the standard deviation of maxweller’s speed is approximately
Two uniform thin rods of equal length 2L and masses M_{1} and M_{2} are joined together along the length. The moment of inertia of the combined rod of length 4L about an axis passing through the mid point and perpendicular to the length of the rod is
A particle is constrained in a onedimensional box of length 2a with potential
Energy difference between level n = 3 and n = 2 is
A person of mass m stands at one end of a plank of mass M and length L. the plank is lying on a smooth horizontal surface, what is distance moves by the plank as the person walks on it to reach the other end.
A particle of mass m is located in a unidimensional potential field where the potential energy of the particle depends on the coordinate x as U(x) = U_{0} (1  cos a x ) ; U_{0} and a are constants. Then the period of small oscillations that the particle performs about the equilibrium position.
If the electrostatic potential at point (x,y) is given by V (x,y) = [ 4x + 9y] volts, the electrostatic energy density at that point (in J/m^{3}) is
A solid sphere of mass m callides head on with identical sphere at rest. If the coefficient of restitution is e. The loss in kinetic energy
An insulated gas jar of mass M which is equal to the molecular mass of the enclosed gas moves with certain K. E. when the jar is stopped, the increment of temperature of the gas is ΔT. The K .E . of the system before stopping is , where adiabatic exponent of the gas.
The input in the below circuit to get output one is
If the amplitude of a damped  oscillator becomes one  third in 2 minutes, what will be the amplitude of oscillation as compared to initial one after 6 minutes ?
The relation between angular frequency ω and wave number K for given type of waves is . The wave number K_{0} for which the phase velocity equals the group velocity is
A ray of light passes through four transparent media with refractive indices μ_{1},μ_{2},μ_{3} and u_{4} as shown in Fig. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have
For a pure substance, the slope of the plot of Gibbs free energy (G) against T at constant pressure is
The space  time coordinates of two events as measured by O are x_{1}= 6 x 10^{4} m,y_{1} = z_{1} = Om, t_{1}’ = 2 x 10^{4}sec and x_{2}= 12 x 10^{4}m, t_{2}= 1 x 10^{4}sec. What must be the velocity of O’ with respect to O if O’ measures the two events to occur simultaneously ?
are the Pauli matrices. The expression equal to
The electric field component of a plane electromagnetic wave travelling in vacuum is given by The Poynting vector for the wave is
The xy plane is the boundary between free space and a magnetic material with relative permeability μ. The magnetic field in the free space is The magnetic field in the magnetic material is
An infinite, conducting slab kept in a horizontal plane carries a uniform charge density σ . Another infinite slab of thickness t, made of a linear dielectric material of dielectric constant K, is kept above the conducting slab. The bound charge density on the upper surface of the dielectric slab is _______ .
Two parallel plates of a capacitor, separated by 2 mm, are at a potential difference of 20V. A dielectric sheet of dielectric constant 2 and thickness 1 mm is inserted between the plates. How does the potential difference between the two plates change ?
If waves in an ocean travel with a phase velocity then what is the group velocity V_{g} of the ‘wave packet’ of these waves ?
A transistor with β = 100 is used in C E configuration.The collector circuit resistance is 1k Ω & V_{cc} = 20v. Assuming V_{be} = 0. Find the value of collector to base resistance such that quiescent collector emitter voltage is 4V.
Calculate the collector current in Voltage divider method with the following data
A truth table is given as, then the correct logic expression corresponding to it is
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