When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes

A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $$\mathrm{cm}$$ is doubled and the current is made $$\left(\frac{1}{3}\right)^{\text {rd }}$$ then the new value of the magnetic field will be

A ray of light is incident at an angle 'I' on one face of thin prism. The ray emerges normally from the other face. Refractive index of the glass prism is '$$n$$' and angle of prism is '$$A$$'. The value of '$$\mathrm{I}$$' is

The temperature difference bewtween two sides of metal plate, $$3 \mathrm{~cm}$$ thick is $$15^{\circ} \mathrm{C}$$. Heat is transmitted through plate at the rate of $$900 \mathrm{~kcal}$$ per minute per $$\mathrm{m}^2$$ at steady state. The thermal conductivity of metal is