Quantum Mechanics Answers

Two rockets of rest length L approach each other with equal speeds of 0.4c. How
long would one rocket appear to the other?

Inside a spacecraft travelling at a speed of 0.8c with respect to the earth, the time
interval between two events on the earth is measured to be 30 hrs. What would the
time interval be if the spacecraft was travelling at a speed of 0.9c.

Show that
[ x,e iap ] = -ae iap
h h

An electron has the following wave function:
¥ (x) = Ae-x (1-e -x)
Determine
i) the normalization constant A, and
ii) the expectation value of x

A student uses an immersion heater to heat some water in a beaker. The water is heated from 20 °C to 80 °C. The energy supplied to the water is 60.0 kJ. What is the thermal capacity of the water? (Ignore any heat loss

Consider a proton as a bound oscillator with a natural frequency of
4 ×10 Hz. 21 
Calculate the energy of its ground and first excited states.

Write an expression for semi-empirical formula for binding energy of nuclei given
by Weizsacker and discuss its each term. Using this formula, calculate the binding
energy per nucleon for
235 U.

Define multiplication factor. When is a reactor said to be supercritical, critical and
subcritical? Write the importance of multiplication factor in a nuclear reactor.

The transition rate of electrons from the first excited state of the hydrogen atom to
the ground state is ~108
/s. What is the minimum range of energies of the resulting
photons that are emitted?

A particle of mass M, initially at rest, decays into two particles with rest masses
m1
and
m2
respectively. Show that the total energy of the mass
m1
is:
M
c M m m
E
2
[ ]
2
2
2
1
2 2
1
 