Energy of an electron in the ground state of the hydrogen atom
Question: Energy of an electron in the ground state of the hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$. Calculate the ionization enthalpy of atomic hydrogen in terms of $\mathrm{J}$ mol $^{-1}$. Solution: It is given that the energy of an electron in the ground state of the hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$. Therefore, the energy required to remove that electron from the ground state of hydrogen atom is $2.18 \times 10^{-18} \mathrm{~J}$. $\therefore$ Ionization entha...
Read More →What is the significance of the terms - ‘isolated gaseous atom’ and ‘ground state’
Question: What is the significance of the terms - isolated gaseous atom and ground state while defining the ionization enthalpy and electron gain enthalpy? Hint:Requirements for comparison purposes. Solution: Ionization enthalpy is the energy required to remove an electron from an isolated gaseous atom in its ground state. Although the atoms are widely separated in the gaseous state, there are some amounts of attractive forces among the atoms. To determine the ionization enthalpy, it is impossib...
Read More →Which of the following potential energy curves in Fig. 6.18 cannot possibly
[question] Question. Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls? Here r is the distance between centres of the balls. [/question] [solution] solution: (i), (ii), (iii), (iv), and (vi) The potential energy of a system of two masses is inversely proportional to the separation between them. In the given case, the potential energy of the system of the two balls will decrease as they come closer to each other. It wi...
Read More →Look at leaves of the same plant on the shady side and compare it with the leaves on the sunny side.
Question: Look at leaves of the same plant on the shady side and compare it with the leaves on the sunny side. Or, compare the potted plants kept in the sunlight with those in the shade. Which of them has leaves that are darker green? Why? Solution: Light is a limiting factor for photosynthesis. Leaves get lesser light for photosynthesis when they are in shade. Therefore, the leaves or plants in shade perform lesser photosynthesis as compared to the leaves or plants kept in sunlight. In order to...
Read More →Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated.
Question: Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated. (a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins. (b) What is the force of friction after perfect rolling begins? Solution: A torque is required to roll the given disc.As per the definition of torque, the rotating force should be tangential to the disc. Since the frictional force at point B is along the tangential force at po...
Read More →Find out how much cellulose is made by all the plants in the biosphere
[question] Question. Find out how much cellulose is made by all the plants in the biosphere and compare it with how much of paper is manufactured by man and hence what is the consumption of plant material by man annually. What a loss of vegetation! [/question] [solution] Solution: Approximately, 100 billion tonnes of cellulose are made per year by all the plants in the biosphere and it takes 17 full grown trees to make one ton of paper. Trees are also used to fulfil the other requirements of man...
Read More →Why is the colour of a leaf kept in the dark frequently yellow, or pale green? Which pigment do you think is more stable?
Question: Why is the colour of a leaf kept in the dark frequently yellow, or pale green? Which pigment do you think is more stable? Solution: Since leaves require light to perform photosynthesis, the colour of a leaf kept in the dark changes from a darker to a lighter shade of green. Sometimes, it also turns yellow. The production of the chlorophyll pigment essential for photosynthesis is directly proportional to the amount of light available. In the absence of light, the production of chlorophy...
Read More →A disc rotating about its axis with angular speed
Question: A disc rotating about its axis with angular speed $\omega_{0}$ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is $R$. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated? Solution: $v_{A}=R \omega_{0} ; v_{B}=R \omega_{0} ; v_{c}=\left(\frac{R}{2}\right) \omega_{o} ;$ The disc will not roll Angular speed of the disc $=\omega_{0}$ Radius of the ...
Read More →Suppose there were plants that had a high concentration of Chlorophyll-b,
Question: Suppose there were plants that had a high concentration of Chlorophyll-b, but lacked chlorophyll-a, would it carry out photosynthesis? Then why do plants have chlorophyll-band other accessory pigments? Solution: Chlorophyll-amolecules act as antenna molecules. They get excited by absorbing light and emit electrons during cyclic and non-cyclic photophosphorylations. They form the reaction centres for both photosystems I and II. Chlorophyll-band other photosynthetic pigments such as caro...
Read More →Explain why cations are smaller and anions larger in radii than their parent atoms?
Question: Explain why cations are smaller and anions larger in radii than their parent atoms? Solution: A cation has a fewer number of electrons than its parent atom, while its nuclear charge remains the same. As a result, the attraction of electrons to the nucleus is more in a cation than in its parent atom. Therefore, a cation is smaller in size than its parent atom. On the other hand, an anion has one or more electrons than its parent atom, resulting in an increased repulsion among the electr...
Read More →RuBisCo is an enzyme that acts both as a carboxylase and oxygenase.
Question: RuBisCo is an enzyme that acts both as a carboxylase and oxygenase. Why do you think RuBisCo carries out more carboxylation in C4plants? Solution: The enzyme RuBisCo is absent from the mesophyll cells of C4plants. It is present in the bundle-sheath cells surrounding the vascular bundles. In C4plants, the Calvin cycle occurs in the bundle-sheath cells. The primary CO2acceptor in the mesophyll cells is phosphoenol pyruvate a three-carbon compound. It is converted into the four-carbon com...
Read More →State whether the following are true or false.
[question] Question. State whether the following are true or false. Justify your answer (i) The value of tan A is always less than 1. (ii) $\sec A=\frac{12}{5}$ for some value of angle $A$. (iii) cos A is the abbreviation used for the cosecant of angle A. (iv) cot A is the product of cot and A. (v) $\sin \theta=\frac{4}{3}$ for some angle $\theta$. [/question] [solution] Solution: (i) False. We know that $60^{\circ}=\sqrt{\mathbf{3}}>\mathbf{1}$. (ii) True. We know that value of $\sec A$ is alwa...
Read More →Even though a very few cells in a C4 plant carry out the biosynthetic
Question: Even though a very few cells in a C4plant carry out the biosynthetic Calvin pathway, yet they are highly productive. Can you discuss why? Solution: The productivity of a plant is measured by the rate at which it photosynthesises. The amount of carbon dioxide present in a plant is directly proportional to the rate of photosynthesis. C4plants have a mechanism for increasing the concentration of carbon dioxide. In C4plants, the Calvin cycle occurs in the bundle-sheath cells. The C4compoun...
Read More →Consider the following species:
Question: Consider the following species: $\mathrm{N}^{3-}, \mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}$ and $\mathrm{Al}^{3+}$ (a) What is common in them? (b) Arrange them in the order of increasing ionic radii. Solution: (a) Each of the given species (ions) has the same number of electrons (10 electrons). Hence, the given species are isoelectronic. (b) The ionic radii of isoelectronic species increases with a decrease in the magnitudes of nuclear charge. The arrangement ...
Read More →By looking at which internal structure of a plant can you tell whether a plant is C3 or C4? Explain.
Question: By looking at which internal structure of a plant can you tell whether a plant is C3or C4? Explain. Solution: The leaves of C4plants have a special anatomy called Kranz anatomy. This makes them different from C3plants. Special cells, known as bundle-sheath cells, surround the vascular bundles. These cells have a large number of chloroplasts. They are thick-walled and have no intercellular spaces. They are also impervious to gaseous exchange. All these anatomical features help prevent p...
Read More →Find out a qualitative test for proteins, fats and oils,
[question] Question. Find out a qualitative test for proteins, fats and oils, amino acids and test any fruit juice, saliva, sweat and urine for them. [/question] [solution] Solution: (a) Test for protein Biuret’s test – If Biuret’s reagent is added to protein, then the colour of the reagent changes from light blue to purple. (b) Test for fats and oils Grease or solubility test (c) Test for amino acid Ninhydrin test – If Ninhydrin reagent is added to the solution, then the colourless solution cha...
Read More →By looking at a plant externally
Question: By looking at a plant externally can you tell whether a plant is C3or C4? Why and how? Solution: One cannot distinguish whether a plant is C3or C4by observing its leaves and other morphological features externally. Unlike C3plants, the leaves of C4plants have a special anatomy called Kranz anatomy and this difference can only be observed at the cellular level. For example, although wheat and maize are grasses, wheat is a C3plant, while maize is a C4plant....
Read More →Prove the result that the velocity v of translation of a rolling body
Question: Prove the result that the velocity $v$ of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height $h$ is given by $v^{2}=\frac{2 g h}{\left(1+k^{2} / R^{2}\right)}$. Using dynamical consideration (i.e. by consideration of forces and torques). Notekis the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane. Solution: A body rollingon an incl...
Read More →In $\triangle P Q R$, right angled at Q,
[question] Question. In $\triangle P Q R$, right angled at $Q, P R+Q R=25 \mathrm{~cm}$ and $P Q=5 \mathrm{~cm}$. Determine the values of $\sin P, \cos P$ and $\tan P$. [/question] [solution] Solution: In figure, PQ = 5 cm PR + QR = 25 cm i.e., PR = 25 cm – QR Now, $\mathrm{PR}^{2}=\mathrm{PQ}^{2}+\mathrm{QR}^{2}$ $\Rightarrow \quad(25-\mathrm{QR})^{2}=(5)^{2}+\mathrm{QR}^{2}$ $\Rightarrow \quad 625-50 \times \mathrm{QR}+\mathrm{QR}^{2}=25+\mathrm{QR}^{2}$ 50 × QR = 600 QR = 12 cm and PR = 25 ...
Read More →What do you understand by isoelectronic species?
Question: What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (i) $\mathrm{F}^{-}$ (ii) $\mathrm{Ar}$ (iii) $\mathrm{Mg}^{2+}$ (iv) $\mathrm{Rb}^{+}$ Solution: Atoms and ions having the same number of electrons are called isoelectronic species. (i) $F^{-}$ion has $9+1=10$ electrons. Thus, the species isoelectronic with it will also have 10 electrons. Some of its isoelectronic species are Na ion ( 11 - $1=10$ electro...
Read More →Which of the following statements are true? If false, correct them:
Question: Which of the following statements are true? If false, correct them: (a) Boron deficiency leads to stout axis. (b) Every mineral element that is present in a cell is needed by the cell. (c) Nitrogen as a nutrient element, is highly immobile in the plants. (d) It is very easy to establish the essentiality of micronutrients because they are required only in trace quantities. Solution: (a)True (b)All the mineral elements present in a cell are not needed by the cell. For example, plants gro...
Read More →Which of the following statements are true? If false, correct them:
Question: Which of the following statements are true? If false, correct them: (a) Boron deficiency leads to stout axis. (b) Every mineral element that is present in a cell is needed by the cell. (c) Nitrogen as a nutrient element, is highly immobile in the plants. (d) It is very easy to establish the essentiality of micronutrients because they are required only in trace quantities. Solution: (a)True (b)All the mineral elements present in a cell are not needed by the cell. For example, plants gro...
Read More →How does atomic radius vary in a period and in a group?
Question: How does atomic radius vary in a period and in a group? How do you explain the variation? Solution: Atomic radius generally decreases from left to right across a period. This is because within a period, the outer electrons are present in the same valence shell and the atomic number increases from left to right across a period, resulting in an increased effective nuclear charge. As a result, the attraction of electrons to the nucleus increases. On the other hand, the atomic radius gener...
Read More →(a) Prove the theorem of perpendicular axes.
Question: (a)Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point $(x, y)$ in the $x-y$ plane from an axis through the origin perpendicular to the plane is $\left.x^{2}+y^{2}\right)$. (b) Prove the theorem of parallel axes. (Hint: If the centre of mass is chosen to be the origin $\sum m_{i} \mathbf{r}_{i}=0$ ). Solution: (a)The theorem of perpendicular axes states that the moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal t...
Read More →In triangle ABC right angled at B
[question] Question. In triangle $\mathrm{ABC}$ right angled at $\mathrm{B}$, if $\tan \mathrm{A}=\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}$, find the value of : (i) $\sin A \cos C+\cos A \sin C$ (ii) $\cos \mathrm{A} \cos \mathrm{C}-\sin \mathrm{A} \sin \mathrm{C}$. [/question] [solution] Solution: $\tan A=\frac{1}{\sqrt{3}}$ $\frac{\mathbf{B C}}{\mathbf{B A}}=\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}$ $\mathrm{BC}=\mathrm{k}$ and $\mathrm{BA}=\sqrt{\mathbf{3} \mathbf{k}}$ $\mathrm{AC}^{2}=\mathrm{BC}^{2...
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