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′
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Determine the commutator [Lz ,Ly ] .
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 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?
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.
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.
State Moseley’s law. Using this law, obtain the frequency of an X-ray line when an L to K transition takes place in a silver atom. Take σ = 3.
Plot a graph between binding energy per nucleon as a function of mass number. Write the main features of the curve.