Electromagnetic Waves

The electric field associated with an electromagnetic wave in vaccum is given by E = i 40 cos (kz − 6 x 10⁸ t), where E, Z and t are in volt m^-1, metre and second respectively. The value of wave vector (k) is

• 2 m^-1

• 0.5 m^-1

• 6 m^-1

• 3 m^-1

Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

• ${\mathrm{\lambda }}_0 = \frac{2{\mathrm{mc\lambda }}^2}{\mathrm{h}}$

• ${\mathrm{\lambda }}_0 = \frac{2\mathrm{h}}{\mathrm{mc}}$

• ${\mathrm{\lambda }}_0 = \frac{2{\mathrm{m}}^2{\mathrm{c}}^2{\mathrm{\lambda }}^3}{{\mathrm{h}}^2}$

• ${\mathrm{\lambda }}_0 = \mathrm{\lambda }$

Which of the following electromagnetic waves have the smallest wavelength ?

• γ-rays

• X-rays

• UV waves

• infrared rays

Two elements A and B with atomic numbers Z_A and Z_B are used to produce characteristic X-rays with frequencies v_A and v_B respectively. If Z_A : Z_B = 1 : 2, then v_A : v_B will be

• $1 : \sqrt{2}$

• 1 : 8

• 4 : 1

• 1 : 4

The condition under which a microwave oven heats up a food item containing water molecules most efficiently is

• the frequency of the microwave must match the resonant frequency of the water molecules

• the frequency of the microwave has no relation with natural frequency of water molecules

• microwave are heat waves, so always produce heating

• infrared waves produce heating in a microwave oven

In which of the following phenomena, the heat waves travel along straight lines with the speed of light ?

• Thermal conduction

• Forced convection

• Natural convection

• Thermal radiation

The energy of gamma (γ) ray photon is E_γ and that of an X-ray photon is E_x. If the visible light photon has an energy of E_v, then we can say that

• E_X > E_γ > E_v

• E_γ > E_v > E_X

• E_γ > E_X > E_v

• E_X > E_v > Eγ