List of top Physics Questions on Solid State Physics asked in GATE PH

Copper has an electron number density of \(8.3 \times 10^{28}\text{ m}^{-3}\). Its Fermi energy in eV (rounded off to one decimal place) is ______.
(\(\hbar = 1.06 \times 10^{-34}\text{ J.s}\), mass of electron \(m_e = 9.10\times 10^{-31}\text{ kg}\), charge of electron \(= 1.60\times 10^{-19}\text{ C}\))

The dispersion (\(E(k)\)) of the conduction band (CB) and valence band (VB) for a semiconductor are shown schematically in the figure. Considering the possibility of an electron making a transition from the bottom of the CB to the top of the VB, which of the following options is/are correct?

Consider a metal-superconductor junction connected to a dc voltage \(V\). At \(T < T_c\), where \(T_c\) is the superconductor's transition temperature, the current \(I\) versus \(V\) behavior of this junction is shown schematically in the figure below.

If the superconducting energy gap is \(D\) meV, the value of \(D\) (rounded off to one decimal place) is

For the energy dispersion of an electron in a one-dimensional solid \(E(k) = E_0 - 2\gamma \cos(ka)\), the ratio of the effective mass of the electron in the solid to the free electron mass (\(m_e\)) at \(k = 0\) is \(R_0\). Taking \(\gamma = 0.5\) eV and \(a = 0.5\) nm, the value of \(R_0\) (rounded off to two decimal places) is
(\(\hbar = 1.054 \times 10^{-34}\) J.s, \(m_e = 9.1 \times 10^{-31}\) kg, electron charge \(= 1.6 \times 10^{-19}\) C)