The energy of a particle of mass m bound by a special kind of spring is
E = p2/2m + kx4
where k is a positive constant. Use the Heisenberg’s Uncertainty Principle to calculate the minimum possible energy of the particle.
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Consider nuclei with small mass number A such that N = Z = A/2 . Neglecting
pairing term (∈) show that semi-empirical formula is given by
Obtain the value of A and Z for which binding energy per nucleon (BE / A) is maximum. Take β = 17.8, δ = 0.71.
In a circular accelerator a proton is accelerated to an energy of 1012 eV, as measured in the laboratory frame. If the rest energy of the proton is 109 eV, calculate
the speed of the proton as measured in the laboratory frame
ii) the force that must be applied by the magnets in the accelerator to keep the
protons moving at this speed in a circle of radius 1000 m.
Two events happen simultaneously in the frame S at a distance of 3.0 light years apart. In the frame S′, which is moving with a speed v relative to S, the distance between these events is 3.5 light years. Calculate (i) v and (ii) the time interval between these events in the frame S′
Plot a graph between binding energy per nucleon as a function of mass number. Write the main features of the curve.
Calculate (x) and (px) for the ground state harmonic oscillator eigenfunction.
In a region of space a particle of mass m has a wavefunction:
where a is a positive constant. Calculate:
i) the normalization constant N
ii) the potential energy of the particle if the total energy of the particle is zero.
The energy of a particle of mass m bound by a special kind of spring is
E = p2/2m + kx4
where k is a positive constant. Use the Heisenberg’s Uncertainty Principle to calculate the minimum possible energy of the particle.