Quantum Mechanics Answers

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

 

wave traveling on the surface of water is composed of elementary harmonic waves of the type: A ex)where the phase velocity is proportional to the square root of its wavelength (provided that λ is less than the depth of the water) In terms of the wave-number k, find the phase velocity and the group velocity of this wave.