Section B
[2 Marks]
Answer: Doping of an intrinsic semiconductor refers to the process of introducing impurities into the semiconductor material to modify its electrical properties. By adding specific atoms, the conductivity of the material can be increased. The two types of atoms used for doping Germanium (Ge) or Silicon (Si) are 'donor' atoms, typically from group V of the periodic table, like phosphorus (P) or arsenic (As), which donate extra electrons, and 'acceptor' atoms, like boron (B), which create holes by accepting electrons.
Key Points: doping process-modifies electrical properties-increases conductivity-donor atoms (group V)-acceptor atoms (group III)
[2 Marks]
Answer: Isotopes are nuclides with the same atomic number (Z) but different neutron numbers (N), which results in different mass numbers (A). For example, 12C and 14C are isotopes of carbon. Isobars, on the other hand, have the same mass number (A) but different atomic numbers (Z), such as 40Ar and 40Ca. Two nuclei with different mass numbers A1 and A2 are not isotopes of the same element, as isotopes must have the same Z.
Key Points: Isotopes: same atomic number, different neutrons; Isobars: same mass number, different atomic numbers; Different A1 and A2 nuclei cannot be isotopes of the same element.
[2 Marks]
Answer: The barrier potential in a p-n junction forms due to the diffusion of charge carriers. When p-type and n-type materials are joined, electrons from the n-region diffuse into the p-region and recombine with holes, leading to a depletion region. This region becomes positively charged on the p-side and negatively charged on the n-side, creating an electric field. The electric field then establishes the barrier potential, preventing further charge carrier movement.
Key Points: Diffusion of charge carriers - Formation of depletion region - Creation of electric field - Establishment of barrier potential
[2 Marks]
Answer: Photoelectric emission from a surface depends on several factors: the intensity of the incident light, the frequency of the light, and the work function of the material. The threshold frequency is the minimum frequency of incident radiation required to emit photoelectrons from a material's surface. Below this frequency, no emission occurs, regardless of light intensity. Different materials have different threshold frequencies based on their work functions.
Key Points: Factors: intensity of light-frequency of light-work function; Threshold frequency: minimum frequency required for emission-no emission below this frequency.
Section C
[3 Marks]
Answer: Bohr's postulates regarding the hydrogen atom state that electrons move in circular orbits around the nucleus due to electrostatic attraction. These orbits are stable because the angular momentum of the electron is quantized, given by L = n(h/2π), where n is a positive integer, and h is Planck's constant. To prove that the speed (v) of the electron in the nth orbit is proportional to (1/n), we start with the centripetal force required for circular motion equated to the electrostatic force. The centripetal force (F) is given by m(v^2/r), where m is the mass of the electron and r is the radius of the orbit. The electrostatic force (F') is given by k(e^2/r^2), where k is Coulomb's constant and e is the charge of the electron. Equating the forces, we get m(v^2/r) = k(e^2/r^2). Rearranging this gives v^2 = k(e^2/m) * (1/r). Since r can be expressed as n^2h^2/(4π^2ke^2m) from Bohr’s model, substituting this back, we find v = (constant)/(n), hence proving v ∝ (1/n).
Key Points: Bohr's postulates explain stable orbits; angular momentum is quantized; relationship between centripetal and electrostatic force; speed of electron derived from radial distance; proved that velocity decreases with increasing n.
[3 Marks]
Answer: Electromotive force (emf) in a solar cell is generated through the photovoltaic effect. When sunlight hits the solar cell, photons are absorbed by the semiconductor material, typically silicon. This absorption provides enough energy to excite electrons, allowing them to break free from their atomic bonds, creating electron-hole pairs. The built-in electric field within the solar cell's p-n junction drives these free electrons towards the n-type layer and holes toward the p-type layer, generating an electric current. The current produced is direct current (DC), and the amount of current output is directly related to the intensity of the incident light. The I-V characteristics of a solar cell are represented graphically by plotting current (I) on the y-axis and voltage (V) on the x-axis, showcasing the relationship between the two. The curve typically shows an initial rising current until it reaches a maximum, beyond which the voltage increases while the current decreases until reaching the open-circuit voltage.
Key Points: Photovoltaic effect-electrons excited by sunlight-electron-hole pairs generated-p-n junction electric field drives charge carriers-I-V characteristics graph shows current vs voltage
[3 Marks]
Answer: To find the speed of a proton in the beam, we can use the kinetic energy formula: KE = (1/2)mv^2. Given that the kinetic energy (KE) is 4.1 MeV, we first convert this energy to joules: 4.1 MeV = 4.1 x 1.6 x 10^-13 J = 6.56 x 10^-13 J. Assuming the mass of a proton, m = 1.67 x 10^-27 kg, we rearrange the formula to solve for speed (v). Thus, v = sqrt((2 * KE) / m) ≈ 1.62 x 10^7 m/s.
To calculate the distance of closest approach (r), we apply the formula r = (1/(4πε₀)) * (Z * e² / KE), where e = 1.6 x 10^-19 C and ε₀ = 8.85 x 10^-12 C²/N·m². Plugging in values, we get: r ≈ 2.34 x 10^-14 m.
Key Points: Convert energy from MeV to Joules - Use KE formula to find speed - Calculate distance of closest approach using electrostatic potential energy equation
[3 Marks]
Answer: i) When orange light is used instead of green light, the angular width of the central maximum increases because orange light has a longer wavelength than green light. According to the formula for angular width, which is directly proportional to the wavelength, using orange light results in a broader central maximum. ii) Moving the screen closer to the slit does not change the angular width; it merely affects the distance at which the diffraction pattern is observed. The angular width remains unchanged as it depends on the slit width and wavelength. iii) Decreasing the slit width increases the angular width of the central maximum. A narrower slit causes greater spreading of light due to diffraction, leading to a wider central maximum.
Key Points: Angular width depends on wavelength; longer wavelengths increase width. Moving the screen affects distance, not width. Decreased slit width increases diffraction, widening the central maximum.
[3 Marks]
Answer: Total internal reflection occurs under two essential conditions: First, the light must travel from a medium of higher refractive index to one of lower refractive index. Second, the angle of incidence must exceed the critical angle for that interface. In the case of prisms ABC and DBC, critical angles are given as 41.1° and 45°, respectively. When light enters prism ABC at an angle greater than 45°, it undergoes total internal reflection and is directed toward prism DBC, following the same principle for angles exceeding 41.1° for the second prism as well.
Key Points: Light from higher to lower index - Angle of incidence must exceed critical angle - Prisms ABC and DBC critical angles 41.1° and 45° - Light reflects and continues through the prisms
[3 Marks]
Answer: When an electron is accelerated through a potential difference of 100 V, it gains kinetic energy equal to the work done by the electric field. The kinetic energy (KE) can be calculated using the formula KE = eV, where e is the charge of the electron (1.6 × 10^-19 C). Thus, KE = 1.6 × 10^-19 × 100 = 1.6 × 10^-17 J. The velocity (v) can be found using the formula KE = 0.5mv², leading to v = sqrt(2KE/m), with m being the mass of the electron (9.11 × 10^-31 kg). For momentum (p), we can use p = mv. The wavelength (λ) is derived from the de Broglie equation λ = h/p, where h is Planck's constant (6.63 × 10^-34 Js). Performing these calculations will give the required values.
Key Points: formula for kinetic energy, potential difference relationship to energy, de Broglie wavelength, electron mass and charge, calculation of velocity and momentum
[3 Marks]
Answer: To calculate the fringe width (β) in Young's double-slit experiment, we use the formula β = λD / d, where λ is the wavelength (600 nm or 600 × 10⁻⁹ m), D is the distance to the screen (1.6 m), and d is the slit separation (0.8 mm or 0.8 × 10⁻³ m). Substituting these values, we get β = (600 × 10⁻⁹ m × 1.6 m) / (0.8 × 10⁻³ m) = 0.0012 m or 1.2 mm.
For the third minimum, the distance from the central maximum is given by y_min = (m + 0.5) × β. For m = 3, y_min = (3 + 0.5) × 1.2 mm = 4.2 mm.
For the fifth maximum, the distance from the central maximum is given by y_max = m × β. For m = 5, y_max = 5 × 1.2 mm = 6 mm.
Key Points: Fringe width formula; Calculation using values; Distance for minimum using m+0.5; Distance for maximum using m
[3 Marks]
Answer: The electromagnetic waves used in the mentioned applications are as follows: (i) For radar systems, the wave is classified as microwave, which operates within the wavelength range of about 1 mm to 1 m. A common source of microwave is a magnetron, which generates microwaves for radar. (ii) In water purifiers, ultraviolet (UV) rays are used, which have a wavelength of about 10 nm to 400 nm. A typical source of UV rays is a mercury vapor lamp. (iii) Lastly, for remote switches used in TVs, infrared (IR) waves, with wavelengths ranging from 700 nm to 1 mm, are utilized. The source of IR waves can be an infrared light-emitting diode (LED).
Key Points: Microwave for radar, source: magnetron - Ultraviolet for water purifiers, source: mercury vapor lamp - Infrared for remote switches, source: infrared LED
[3 Marks]
Answer: In a converging lens, magnification is defined as the ratio of the image height to the object height. It is positive when the object is placed between the focal point and the lens, resulting in an upright, virtual image. Conversely, the magnification becomes negative when the object is beyond the lens's focal point, producing an inverted real image. For part (b), if we consider the point object placed at O in front of a glass sphere, the image formation occurs due to refraction at the surfaces of the sphere, resulting in a real image on the opposite side of the object.
Key Points: Magnification positive: object between lens focus and lens; Magnification negative: object beyond lens focus; Formation of image in glass sphere: refraction at sphere surfaces
[3 Marks]
Answer: For two light sources to be coherent, they must fulfill two primary conditions: first, they should have the same frequency, which ensures that they oscillate at identical rates, thereby producing a consistent wave pattern over time. Second, there must be a stable phase difference between them, meaning the relative position of their peaks and troughs remains constant. This coherence allows for the formation of a clear interference pattern. In contrast, an interference pattern from a double-slit setup exhibits equally spaced bright and dark fringes due to coherent sources, while a diffraction pattern from a single slit contains a central maximum with gradually diminishing side maxima, demonstrating the effects of wave spreading.
Key Points: same frequency; stable phase difference; double-slit shows equally spaced fringes; single-slit has a central maximum with diminishing side maxima