Calculate the temperature at which the number of electrons in the conduction band of a semiconductor is four times the number at room temperature. Take the band gap energy to be

For the energy dispersion relation:calculate the inverse mass tensor and the group velocity given m1 = 3m2 .

calculate the inverse mass tensor and the group velocity given m1 = 3m2 .

satisfies the Bloch theorem. 

For a free electron gas in two dimensions, derive the relation between the number density of electrons and the Fermi wave vector.

Metallic sodium is monovalent and crystallizes in a bcc structure with a lattice constant of 4.25 Å . Calculate the number density of conduction electrons and the Fermi energy at 0 K.

Debye temperature for diamond is 2230 K. Calculate the frequency of highest possible lattice vibration in diamond and its molar heat capacity at 20 K.

If the potential energy function is expressed ascalculate the inter molecular distance at which the potential energy is a minimum. Show that in the stable configuration the energy of attraction is eight times the energy of repulsion.

At what angle will a diffracted beam emerge from the (110) planes of a cubic crystal of unit cell length 0.6 nm? Assume diffraction occurs in the first order and that the X-ray wavelength is 0.154 nm ?

Show that the volume of the primitive cell in the reciprocal lattice space is inversely proportional to the volume of the primitive cell in the direct lattice.

A metallic element has a density of 7.15 g cm³, a lattice constant of 2.880 A and an atomic weight of 51.9961. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure.

Use the Gauss elimination method to solve the system of equations:

Determine the first eight random numbers generated by using the linear congruential random number generator with a=c=7 and m=10. What is the period of this random number sequence.

Use Euler’s method for the differential equationwith the initial condition y(0) = 2 to calculate y(2) . Take a value of step size h =0.5 .

Using the trapezoidal rule, estimate the value of the integra and the true error.

Explain why one should not use higher order polynomial interpolation. What would be a preferable method of using information from several data points for interpolation?

Given the following data for the velocity as a function of time, calculate the velocity at

t = 12 s using second order polynomial interpolation in the Newton divided 

difference method:

In what way is the Newton-Raphson method more beneficial than the bisection method?

What are the advantages and drawbacks of the bisection method?

Use the bisection method in the interval [2,4] to calculate the root/s of the equation

 up to three iterations. Calculate the absolute relative approximate error at each stage.

The approximate value of the derivative of a functionat x can be calculated using formula: 

Calculate 

Determine the true error and relative true error in each case

Define true error and relative true error