CBSE EXAMINATION PAPER-2022
PHYSICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 14 questions. All questions are compulsory.
- This question paper is divided into 2 sections.
- Section A – questions number 1 to 4 are very short answer
- Section B – questions number 5 to 14 are short answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
(a) (i) Define the terms : ' impact parameter' and 'distance of closest approach' for an α -particle in Geiger-Marsden scattering experiment.
(ii) What will be the value of the impact parameter for scattering angle (I) θ= 0 degree and (II) θ= 180 degree?
(b) Photoelectric emission occurs when a surface is irradiated with the radiation of frequency (i) v1, and (ii) v2. The maximum kinetic energy of the electrons emitted in the two cases are K and 2K respectively. Obtain the expression for the threshold frequency for the surface.
Section B
(a) (i) Depict a plane electromagnetic wave propagating along the x-axis. Write the expressions for its oscillating electric and magnetic fields.
(ii) Write three characteristics of electromagnetic waves.
(a) State the conditions for total internal reflection to take place.
(b) A tank is filled with a transparent liquid to height 'H'. A coin suspended by a thread in the liquid is gradually lowered till it touches the bottom. The apparent depth is determined corresponding to different positions of the coin.
(i) Plot a graph showing variation of the apparent depth with the real depth of the coin.
(ii) What is the physical significance of the slope of the graph ?
(a) Draw a labelled ray diagram showing the formation of an image by an astronomical refracting telescope in normal adjustment. Hence, obtain the expression for its magnifying power.
A converging lens made of glass ( μ= 1·5) has its spherical faces of radii of curvature 10 cm and 20 cm. Find its focal length
(a) in air, and
(b) when it is immersed in a liquid of refractive index 1·25.
The energy of a hydrogen atom in the first excited state is -3.4 eV. Find :
(a) the radius of this orbit. (Take Bohr radius = 0·53 Å)
(b) the angular momentum of the electron in the orbit.
(c) the kinetic and potential energy of the electron in the orbit.
(a) Depict the variation of the potential energy of a pair of nucleons with the separation between them.
(b) Imagine the fission of a 56 /26Fe into two equal fragments of 28 /13 Al nucleus. Is the fission energetically possible ? Justify your answer
by working out Q value of the process.
Given : m 56 /26 Fe = 55·93494 u, m 28/ 13 Al = 27·98191 u.
Find the ratio of the de Broglie wavelengths associated with an alpha particle and a proton, if both
(a) have the same speeds,
(b) have the same kinetic energy,
(c) are accelerated through the same potential difference.
(a) When both have the same speed v,
de Broglie wavelength λ = h / (mv), so ratio λ_alpha / λ_proton = m_proton / m_alpha.
Given m_alpha = 4 m_proton,
ratio = 1 / 4.
(b) When both have the same kinetic energy K,
K = (1/2) m v2, so v = sqrt(2K/m).
Therefore λ = h / (m v) = h / (m sqrt(2K/m)) = h / sqrt(2Km).
Ratio λ_alpha / λ_proton = sqrt(m_proton / m_alpha) = sqrt(1/4) = 1/2.
(c) When both are accelerated through the same potential difference V,
kinetic energy gained K = q V.
Both have charge magnitude q, so K_alpha = K_proton.
Thus same as part (b), ratio λ_alpha / λ_proton = 1/2.
Summary:
(a) λ_alpha / λ_proton = 1/4
(b) λ_alpha / λ_proton = 1/2
(c) λ_alpha / λ_proton = 1/2
With the help of a circuit diagram, explain the working of a p-n junction diode as a full-wave rectifier. Also draw its input and output waveforms.
(b) Name the electromagnetic waves which are produced by the following :
(i) Radioactive decays of nucleus
(ii) Welding arcs
(iii) Hot bodies
Write one use each of these waves.
(b) A plane wavefront of light of wavelength 'λ' is incident normally on a narrow slit of width 'a' and a diffraction pattern is observed on a screen at a distance 'D' from the slit.
(i) Depict the intensity distribution in the pattern observed.
(ii) Obtain the expression for the first maximum from the central maximum.
(ii) The positions of minima are given by a sin θ = m λ. The secondary maxima lie between these minima approximately at angles θ satisfying a sin θ = (m + 0.5) λ, where m = 1, 2, ... The first maximum from the central maximum occurs approximately at sin θ = 3 λ / 2a, but for small angles the exact position requires solving dI/dθ = 0. However, approximately, the first maximum occurs near θ where a sin θ = 3 λ / 2. This gives the position of the first secondary maximum from the central peak.
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