Suppose that the electric field amplitude of an electromagnetic wave is E₀ = 120N/C and that its frequency is v = 50.0 MHz.
(a) Determine B₀, \(\omega \) , k and \(\lambda \).
(b) Find expressions for E and B.

(i) Obtain the conditions for the bright and dark fringes in diffraction pattern due to a single narrow slit illuminated by a monochromatic source. Explain clearly, why the secondary maxima go on becoming weaker with increasing of their order?
(ii) When the width of the slit is made double, how would this affect the size and intensity of the central diffraction band? Justify your answer. 

(i) In a double slit experiment using light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is \(0.1^o\) . Find the spacing between the two slits.
(ii) Light of wavelength 5000\(\dot { A } \) propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?

Ajeet's younger brother was just seeing class 12th books. He wondered to know the structure of atoms and arrangement of electrons and protons in them. As he was a class 6th student, he did not understand the whole concept of atomic structure. Ajeet helped him to understand the structure of atoms.
Read the above passage and answer the following questions:
(i) What are the values shown by Ajeet?
(ii) On which metal Rutherford performed \(\alpha \) - particles scattering experiment?
(iii) How Rutherford concluded that at the centre of atom there is massive nucleus which contains positive charge?

Write the truth table for a NAND gate connected as given in the figure. Hence, identity the exact logic operation carried out by this circuit.