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Cathode rays are streams of electrons emitted from the cathode (negative electrode) in a vacuum tube. Cathode rays can be deflected by magnetic and electric fields, demonstrating their charge and nature as electrons.

E = hf + W\(_o\) E = 1.12 x 10\(^{-18}\)J Max. Energy = 8.0 x 10\(^{-19}\)J. W\(_o\) = E - Max. Energy = 1.12 x 10\(^{-18}\)J - 8.0 x 10\(^{-19}\)J. = 3.2 x 10\(^{-19}\)J. But W\(_o\) = hf\(_o\) f\(_o\) = \(\frac{W_o}{h}\) = \(\frac{3.2 \times 10^{-19}}{6.626 \times 10^{-34}}\) = 4.83 x 10\(^{14}\)Hz

(a) electrons are only emitted when the photon frequency exceeds the threshold frequency, - the energy of each photon is proportional to its frequency, - the emission of photoelectrons depends on the frequency of incident light on the metal, - the intensity of light does not affect the energy of the electrons emitted/photoelectrons, - the energy of the photoelectron depends on the frequency of incident radiation. (b) Given: P = 6 x 10\(^{-3}\) W, no of photons per seconds = 1 x 10\(^{16}\), m\(_e\) = 9.1 x 10\(^{-31}\) kg, e = 1.6 x 10\(^{-19}\) C, W\(_o\) = ? Photon Energy E = \(\frac{\text{power}}{\text{no of photons per second}}\) = \(\frac{\text{P}}{\text{n}}\) = \(\frac{6.0 \times 10^{-3}}{1 \times 10^{16}}\) = 6 x 10\(^{-19}\)J But K.E = E + W\(_o\) W\(_o\) = E - K.E = E - eV W\(_o\) = 6 x 10\(^{-19}\) - 2.2 x (1.6 x 10\(^{-19}\)) = 2.48 x 10\(^{-9}\)J (c) Factors on which radioactive activity depends are: (i) decay constant, (ii) number of unstable nuclei present at a given time (iii) time of the decay process (iv) environmental conditions, (v) type of radioisotope, etc (d) Given: A = 2.0 x 10\(^6\)Bq, t\(_{\frac{1}{2}}\) = 1.8 x 10\(^8\)s A = \(\lambda\)N, where \(\lambda\) = decay constant, N = number of radioactive nuclei, A = activity. But \(\lambda\) = \(\frac{In(2)}{t_{\frac{1}{2}}}\) \(\lambda\) = \(\frac{In(2)}{1.8 \times 10^8}\) ≈ \(\frac{0.693}{1.8 \times 10^8}\) ≈ 3.85 x 10\(^{-9}\)s\(^{-1}\) Recall, A = \(\lambda\)N N = \(\frac{A}{\lambda}\) = \(\frac{2.0 \times 10^6}{3.85 \times 10^{-9}}\) = 5.2 x 10\(^{14}\) nuclei

A rectifier is a device that converts alternating current (AC) into direct current (DC). It enables the flow of current in one direction while blocking it in the opposite direction, thus transforming AC voltage into a form of DC voltage suitable for different applications.

Doping involves introducing specific impurities into a semiconductor to modify its electrical properties, enhancing its conductivity by creating either n-type or p-type semiconductors. Rectification is the process of converting alternating current (AC) into direct current (DC) using diodes, which allow current to flow in one direction. Emission refers to the release of charge carriers (electrons or holes) from a semiconductor, often resulting in the production of light in devices like LEDs Stabilization involves techniques to maintain the consistent performance of semiconductor devices under varying conditions.

Conductor: Has a very small or negligible band gap, allowing electrons to move freely. Insulator: Has a large energy gap (typically greater than 3 eV), which prevents electrons from jumping from the valence band to the conduction band, resulting in very low electrical conductivity. Semiconductor: A moderate energy gap (about 1 eV) allows some conductivity under certain conditions (like temperature or doping). Intrinsic Semiconductor: A type of semiconductor with a pure form, that also has a moderate energy gap similar to other semiconductors.

X-rays are typically used for medical imaging and other applications related to examining structures, but they are not used to determine the depth of a mine

X-rays are usually produced by electronic transitions within atoms, whereas gamma rays are released from an atom's nucleus during radioactive decay.

The correct sequence of ionization power from highest to lowest is: Alpha particle > Beta particle > Gamma ray.

To show that \(\lambda\) = \(\frac{\text{h}}{\sqrt{2meV_o}}\) The de broglie wavelength \(\lambda\), is given by \(\lambda\) = \(\frac{\text{h}}{\text{p}}\) where p = mv \(\lambda\) = \(\frac{\text{h}}{\text{mv}}\) When an electron is accelerated through a potential difference V\(_0\), it gains kinetic energy given K.E.= eV\(_0\) The kinetic energy can also be expressed in terms of the mass m of the electron and its speed v: K.E = \(\frac{1}{2}\)mv\(^2\) K.E = eV\(_0\) = \(\frac{1}{2}\)mv\(^2\) v = \(\sqrt{\frac{2eV_o}{m}}\) Substituting v = \(\sqrt{\frac{2eV_o}{m}}\) into the de Broglie equation \(\lambda\) = \(\frac{\text{h}}{m \times \sqrt{\frac{2eV_o}{m}}}\) = \(\frac{\text{h}}{\sqrt{\frac{2eV_o m^2}{m}}}\) \(\lambda\) = \(\frac{\text{h}}{\sqrt{2meV_o}}\) Note: use the fact that \(\sqrt{m}\) x \(\sqrt{m}\) = m

Observations show that when the light travels from a medium A(air) to a more dense medium B(water), the refracted ray bends towards the normal and the angle of refraction (r) is, therefore, less than the angle of incidence. vice versa.

Concave mirrors are designed to focus sunlight onto a specific area, enhancing the intensity of the solar energy. This concentrated energy can then be utilized for heating or converted into electricity in solar thermal and photovoltaic systems.

Concave Mirror: A concave mirror can focus light rays, allowing for a magnified image of the face. This magnification helps in seeing details more clearly, which is particularly useful for shaving. Convex Mirror: A convex mirror creates a smaller, wider image, which is not suitable for precise tasks like shaving. Plane Mirror: A plane mirror shows a true reflection but does not magnify, making it less effective for grooming. Parabolic Mirror: Parabolic mirrors are used for specific applications, like telescopes, but not for shaving.

Under red light, the shirt reflects the red light but does not reflect other colors, which makes it look less vibrant or pale, compared to being illuminated by white light that contains all colors.

Fiber optics: Fiber optics: Utilizes total internal reflection to transmit light through optical fibers, allowing for efficient data transfer.