Calculate (x) and (px) for the ground state harmonic oscillator eigenfunction.
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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.
A radioactive substance of 1 g is reduced to 2.1 mg in 5 years by alpha decay. Calculate the half-life of the substance.
Using the properties: Charge (Q), Lepton number (L), Baryon number (B) show that whether the following processes are allowed or not?
K − + p → Ω¯ + K + + K 0
π+ + p → p + p + ¯n
Calculate the de Broglie wavelength of an electron accelerated by a potential of 1000 V. Also calculate the wavelength of the X-rays that would be produced when these electrons strike a solid.
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.
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′
A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship emits light of wavelength λ = 4500 Å which appears blue to a passenger on the spaceship. What colour would the light appear to a person on earth?