NCERT

Light of wavelength 488 \mathrm{~nm} is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 \mathrm{~V}. Find the work function of the material from which the emitter is made.

Wavelength of light produced by the argon laser is given as $\lambda=488 \mathrm{~nm}=488 \times 10^{-9} \mathrm{~m}$ Stopping potential of the photoelectrons is given as...

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What can be inferred from the magnetic moment values of the following complex species?
Example            Magnetic Moment (BM)
K4[Mn(CN)6)          2.2
[Fe(H2O)6]2+            5.3
K2[MnCl4]               5.9

Magnetic moment is calculated by the formula: ν=[n(n+2)​]1/2 For value n = 1, ν=[1(1+2)]1/2​= (3)1/2 ​= 1.732 For value n = 2, ν=[2(2+2)]1/2​= (8)1/2 ​= 2.83 For value n = 3, ν=[3(3+2)]1/2 ​=...

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A 100 \mathrm{~W} sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength
of the sodium light is 589 \mathrm{~nm} . (a) What is the energy per photon associated with the sodium light? (b) At what rate are the photons delivered to the sphere?

Power of the sodium lamp is given as $\mathbf{P}=\mathbf{1 0 0 W}$ Wavelength of the emitted sodium light is given as $\lambda=589 \mathrm{~nm}$ $=589 \times 10^{-9} \mathrm{~m}$ Planck's constant,...

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Compare the general characteristics of the first series of the transition metals with those of the second and third series metals in the respective vertical columns. Give special emphasis on the following points: (i) ionisation enthalpies and (ii) atomic sizes

In each of the three transition series, generally the first ionisation enthalpy increases from left to right. However, there are some exceptions. The first ionisation enthalpies of the third...

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Compare the general characteristics of the first series of the transition metals with those of the second and third series metals in the respective vertical columns. Give special emphasis on the following points: (i) electronic configurations (ii) oxidation states

(i) In the 1st, 2nd and 3rd transition series, the 3d, 4d, and 5d orbitals are filled with electrons respectively. We know that elements in the same group generally have similar electronic...

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Figure below shows a biconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Answer – According to the question –  Focal length of the given convex lens is f1 = 30 cm Since, the liquid acts as a mirror. Focal length of the liquid is denoted by f2 Total focal length...

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Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in Fig. 9.36. A current in the coil produces a deflection of 3.5° of the mirror. What is the displacement of the reflected spot of light on a screen placed 1.5 m away?

Answer – According to the question –  Angle of deflection is θ = 3.5° The distance of the screen from the mirror is D = 1.5 m The deflection undergone by the reflected rays are twice the angle...

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A Cassegrain telescope uses two mirrors as shown in Fig. 9.33. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?

Answer - Below is the diagram of a Cassegrain telescope. It has a concave and a convex mirror. We are given – Distance between the secondary mirror and the objective mirror is d = 20 mm Radius of...

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The virtual image of each square in the figure is to have an area of 6.25 mm2. Find out, what should be the distance between the object in Exercise 9.30 and the magnifying glass?If the eyes are too close to the magnifier, would you be able to see the squares distinctly?

Answer – According to the question – Area of the virtual image of each square is A = 6.25 mm2 Area of each square is A0 = 1 mm2 Hence, the linear magnification of the object can be determined...

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A person looking at a cloth with a pattern consisting of vertical and horizontal lines is able to see the vertical lines more distinctly than the horizontal ones. What is this defect due to? How is such a defect of vision corrected?

Answer – The person in the circumstance is having trouble seeing the horizontal lines, but the vertical lines are clearly apparent. When the eye's refracting system does not work in the same way for...

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For a normal eye, the far point is at infinity and the near point of distinct vision is about 25cm in front of the eye. The cornea of the eye provides a converging power of about 40 dioptres, and the least converging power of the eye-lens behind the cornea is about 20 dioptres. From this rough data estimate the range of accommodation (i.e., the range of converging power of the eye-lens) of a normal eye.

Answer: We have –Least distance of distinct vision is d = 25 cmFar point of a normal eye is d’ = ∞Converging power of the cornea is $P_{c}=40D$Least converging power of the given eye-lens is...

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You are given prisms made of crown glass and flint glass with a wide variety of angles.
Suggest a combination of prisms which will
(i) deviate a pencil of white light without much dispersion,
(ii) disperse (and displace) a pencil of white light without much deviation.

Answer - (i) The two prisms must be in close proximity to one another. The bases of these two prisms must be on opposite sides of the white light that is incident. White light is dispersed for the...

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(i) Figure below shows a cross-section of a ‘light pipe’ made of a glass fiber of refractive
index 1.68. The outer covering of the pipe is made of a material of refractive index
1.44. What is the range of the angles of the incident rays with the axis of the pipe
for which total reflections inside the pipe take place, as shown in the figure.
(ii) What is the answer if there is no outer covering of the pipe?

Answer – (i) Refractive index of the glass fibre is = $\mu_{2}$= 1.68 Refractive index of the outer covering of thr pipe is = $\mu_{1}$= 1.44Angle of incidence is iAngle of refraction is rAngle...

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A small pin fixed on a tabletop is viewed from above from a distance of 50 cm. By
what distance would the pin appear to be raised if it is viewed from the same point
through a 15 cm thick glass slab held parallel to the table? Refractive index of glass =
1.5. Does the answer depend on the location of the slab?
Answer:

According to the question,The actual depth of the pin is d = 15 cmApparent depth of the pin is = d’Refractive index of glass is $\mu$=1.5 here, the ratio of actual depth to the apparent depth and...

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A person with a normal near point (25 cm) using a compound microscope with objective of focal length 8.0 mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0 mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope,

Answer: According to the question, Focal length of the given objective lens is $ f_{o}$= 8 mm = 0.8 cm Focal length of the eyepiece is $ f_{e}$= 2.5 cm Object distance for the given objective lens...

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A compound microscope consists of an objective lens of focal length 2.0cm and an eyepiece of focal length 6.25cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25 cm), and (b) at infinity? What is the magnifying power of the microscope in each case?

Answer: According to the question, we have – Focal length of the given objective lens is f1=2.0 cm Focal length of the given eyepiece is f2=6.25 cm Distance between the eyepiece and the objective...

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A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?

Answer : According to the question, the object given is virtual and the image formed is real. Object distance is u= +12 cm (i) The focal length of the convex lens is f =20 cm Image distance is...

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A prism is made of glass of unknown refractive index. A parallel beam of light is incident on the face of the prism. The angle of minimum deviation is measured to be 40°. What is the refractive index of the
material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.

Answer: We are given that – Angle of minimum deviation is  $\delta_{m}=40°$ Angle of the prism is  A = $60°$ Refractive Index of water is given by, $\mu=1.33$ Material’s refractive Index =...

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A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)

Answer : We are given the following information – Bulb’s actual depth in water is d1=80 cm =0.8 m Refractive Index of water is $\mu$= 1.33 I is the Angle of incidence r is the Angle of refraction –...

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The figures above show the refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence
in water is 45° with the normal to a water-glass interface.

For the glass-air interface, we are given that – Angle of incidence is i =60° Angle of refraction is r=35° Using Snell’s law, the refractive index of the glass with respect to air becomes –...

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A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If
water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

Answer: We are given that Actual depth of the needle in water here is h1=12.5cm Apparent depth in water is h2 =9.4 cm Refractive Index of water is given by – $\mu$ The value of $\mu$ can be...

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A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

Answer – We are given that, Height of the candle is h =2.5 cm Let the image size be h’ Object distance is u = -27 cm Radius of the concave mirror, is R = -36 cm Focal length of the concave mirror...

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Give examples and suggest reasons for the following features of the transition metal chemistry:
(i) The lowest oxide of transition metal is basic, the highest is amphoteric/acidic.
(ii) A transition metal exhibits highest oxidation state in oxides and fluorides.

(i) In the case of a lower oxide of a transition metal, the metal atom has a low oxidation state. This means that some of the valence electrons of the metal atom are not involved in bonding. As a...

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Primary alkyl halide C4H9Br (a) reacted with alcoholic KOH to give compound (b). Compound (b) is reacted with HBr to give (c) which is an isomer of (a). When (a) is reacted with sodium metal it gives compound (d), C8H18 which is different from the compound formed when n-butyl bromide is reacted with sodium. Give the structural formula of (a) and write the equations for all the reactions.

The formula C4H9Br is used to make two main alkyl halides. They're n-butyl bromide and isobutyl bromide, respectively. Compound (a) is therefore either nbutyl bromide or isobutyl bromide. Compound...

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Arrange the compounds of each set in order of reactivity towards SN2 displacement: (i) 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane (ii) 1-Bromo-3-methylbutane, 2-Bromo-2-methylbutane, 3-Bromo-2- methylbutane (iii) 1-Bromobutane, 1-Bromo-2,2-dimethylpropane, 1-Bromo-2-methylbutane, 1Bromo-3- methylbutane.

(i) The nucleophile approaches the carbon atom to which the leaving group is linked in an SN2 reaction. The reactivity for SN2 displacement reduces when the nucleophile is sterically inhibited. The...

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Predict all the alkenes that would be formed by dehydrohalogenation of the following halides with sodium ethoxide in ethanol and identify the major alkene: (i) 1-Bromo-1-methylcyclohexane (ii) 2-Chloro-2-methyl butane (iii) 2,2,3-Trimethyl-3-bromopentane.

(i) 1−bromo−1−methylcyclohexane In the given molecule, all β-hydrogens are equivalent. As a result, only one alkene is produced when the given molecule is dehydrogenated. (ii) Different sets of...

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For M2+/M and M3+/M2+ systems the EV values for some metals are as follows:
Cr2+/Cr = -0.9V       Cr3/Cr2+ = -0.4 V
Mn2+/Mn = -1.2V    Mn3+/Mn2+ = +1.5 V Fe2+/Fe = -0.4V Fe3+/Fe2+ = +0.8 V Use this data to comment upon: (i) the stability of Fe3+ in acid solution as compared to that of Cr3+ or Mn3+ and (ii) the ease with which iron can be oxidised as compared to a similar process for either chromium or manganese metal.

(i) The reduction potentials for the given pairs increase in the given order: Mn2+ / Mn < Cr2+ / Cr < Fe2+ /Fe So, the oxidation of Fe to Fe2+ is not as easy as the...

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Answer the following questions:
(a) When a low flying aircraft passes overhead, we sometimes notice a slight shaking of the picture on our TV screen. Suggest a possible explanation.
(b) As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?

Answer – (a) The aircraft's weak radar emissions interfere with the antenna's reception of the TV signal. (b) This is because the linear aspect of a differential equation that drives wave motion...

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A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

Answer – We are given that, λ = 500 nm is the wavelength of the beam of light D= 1 m is the distance between the slit and the screen x = 2.5 mm = 2.5 x 10-3 m is the distance of the first...

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Answer the following questions:
(a) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?
(b) In what way is diffraction from each slit related to the interference pattern in a double-slit experiment?
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?
(d) Two students are separated by a 7 m partition wall in a room 10 m high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily?
(e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in an understanding location and several other properties of images in optical instruments. What is the justification?

Answer – (a) In a single slit diffraction experiment, doubling the slit width reduces the size of the central diffraction band by half while increasing the intensity of the band by four times. (b)...

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For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest; observer moving, and (ii) source moving; observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however, strictly identical for these situations. Explain why this should be so. Would
you expect the formulas to be strictly identical for the two situations in the case of light travelling in a medium?

Answer – Because sound waves can only move through the medium, the Doppler formula differs somewhat between the two scenarios. In both circumstances, the observer's motion relative to the medium is...

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Let us list some of the factors, which could possibly influence the
speed of wave propagation:
(i) nature of the source.
(ii) the direction of propagation.
(iii) the motion of the source and/or observer.
(iv) wavelength.
(v) the intensity of the wave. On which of these factors, if any, does (a) the speed of light in a vacuum,
(b) the speed of light in a medium (say, glass or water), depend?

Answer – (a) In the vacuum, none of the components listed affect the speed of light. (b) The wavelength of light in a media affects the speed of light in that medium.

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You have learnt in the text how Huygens’ principle leads to the laws of reflection and refraction. Use the same principle to deduce directly that a point object placed in front of a plane mirror produces a virtual image whose distance from the mirror is equal to the object distance from the mirror.

Answer – Consider an item O placed at a distance r in front of the plane mirror MO'. The object is designated as point O, and a circle is drawn around it, just touching the plane mirror at point O'....

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Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

Answer – The velocity of light in the denser medium (water) is greater than the velocity of light in the rarer medium (air), according to Newton's Corpuscular hypothesis (vacuum). This was erroneous...

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In a double-slit experiment, 0.2° is found to be the angular width of a fringe on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be ¾.

Answer: We are given, Distance of the screen from the slits is D = 1m Wavelength of light used is λ1​ = 600 nm Angular width of the fringe in air is θ1​ = 0.2° θ2​ is the angular...

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In Young’s double-slit experiment, 0.28mm separation between the slits and the screen is placed 1.4m away. 1.2cm is the distance between the central bright fringe and the fourth bright fringe. Determine the wavelength of light used in the experiment.

Answer – We are given, Distance between the screen and the slits, D = 1.4 m Distance between the slits is d = 0.28 mm = 0.28 x 10-3 m Also, the distance between the central fringe and the...

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