If σ x, σ y and σz are three components of a Pauli spin matrix σ, then show tha
[σ x , σ y ] = 2i σ z ; [σ y , σ z ] = 2iσ x
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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.
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.
State the selection rules for allowed transitions in multielectrons atoms
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.
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.
Calculate (x) and (px) for the ground state harmonic oscillator eigenfunction.