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The quality of mercy is not strain’d

(d) William Shakespeare

Mercy is compared to gentle rain showered from heaven. This comparison is suitable or more apt because mercy also flows like a drop in the hearts of the person.

Usually, the persons who heard any advise from others wouldn’t respond like grandma, The odd in the grandma’s reply was, she said that she will grow disgracefully and she can do it in a better way.

Yes, it had happened. One day when others were in town she had a terrible fall. But the effect of this was the opposite. Instead of fearing, the grandma climbed the tree and made up her mind that she wouldn’t come down.

(1) gift – lift 

(2) told – old 

(3) agree – tree 

(4) ail – fall 

(5) right – tonight

Both the narrator and his father were considerate towards grandma. This shows in the following lines.

 “When granny asked the house on a treetop father said …………… That’s all right you’ll have what you want, dear. I’ll start work tonight. With my expert assistance, he soon finished the chore.” Narrator’s role 

“I climb to her room with glasses and tray ……………. and drinks sherry with me”.

Here the poet suggested or explained that the granny enjoyed to sit in a tree and she felt very uncomfortable and sad if she were in life.

(a) Given,

The charge on 1^st sphere (q₁ ) and 2^nd sphere (q₂) is 0.4 µC or 0.4 × 10^-6 C and -0.8 × 10^-6C respectively.

The electrostatic force on the 1^st sphere is given by F = 0.2N.

Electrostatic force between the spheres is given by the relation :

F = 1/4πϵo​ * q1q2/r²

Here,

ϵ_o​ = permittivity of free space and,

1/4πϵ_o​ = 9 × 10⁹ Nm²C^-2

r² = 1/4πϵ_{o ​}​* q1​q2/F​​

= 0.4*10^-6*8*10^-6*9*10⁹ / 0.2  = 144*10^-4

r = ​√144 x 10^-4 = 12 x 10^-2 = 0.12m

Therefore, the distance between the two spheres = 0.12 m

(b) Since the spheres have opposite charges, the force on the second sphere due to the first sphere will also be equal to 0.2N.

Electric flux through whole cube = \(\cfrac{Q}{\varepsilon_0}\). Electric flux through one face = \(\cfrac16\cfrac{Q}{\varepsilon_0}\mu\) Vm.

(a) Meaning 

The amount of time as well as reason for using the internet may become a matter of concern for e.g., online gambling, gaming, etc. The person may socialise more online with friends than real life socialising. Spending excess time online may cause the person to neglect family, relationships, work etc. Virtual world enables games/gambling almost continuously. This leads to the person neglecting personal hygiene, real life relationships and become withdrawn and irresponsible. The person may feel guilty or defensive about internet use. He/ she may panic in the absence of internet service. A growing dependence on internet refers to an inability to stop and down down.

(b) Four C’s to identify excessive internet usage 

Excessive internet usage is characterised by extensive, problematic addiction to the use of computer and internet. It signifies poorly controlled preoccupations or behaviour regarding such usage. Excessive internet usage leads to personal distress and social impairment. The four C’s to identify excessive internet usage are as follows

1. Craving – Do you have an intense desire to use the internet? 

2. Control – Do you have an inability to control your self using the internet? 

3. Compulsion – Do you find it difficult to stop using the internet? Even though you know you should not spend so much time on it? 

4. Consequence – Have you ever experienced any physical or psychological ill effects as a result of excessive use of the internet? If you answer a ‘yes’ for at least three of the C’s, it can be a matter of concern.

(c) Red flags that indicate internet addiction 

The Red Flags that indicate over dependence on internet are

1. Feelings of euphoria while using the internet. 

2. Physical symptoms like headache, dry eyes, etc.

3. Inability to keep to schedules and boredom with routine tasks. 

4. Poor personal hygiene and nutrition to remain online.

Signs that help to identify individuals who show deviance or distress and require help in mental health are called red flags.

The ‘red flags’ that indicate over dependence on internet are:

1. Feelings of euphoria while using the internet. 

2. Physical symptoms like headache, dry eyes, etc. 

3. Inability to keep to schedules and boredom with routine tasks. 

4. Poor personal hygiene and nutrition to remain online.

(i) 1.77 x 10¹¹ कूलॉम/किग्रा

Stress = Young's modulus x strain = Y x α

Elastic potential energy per unit volume is

u = 1/2 x stress x strain = 1/2 x Y x α x α = 1/2 x Y x α²

Correct option is: (C) \(\sqrt{\frac{2E}{Y}}\)

Correct option is: (A) 0.42 × 10¹¹ N/m²

The fundamental is the first harmonic. Therefore, the ratio of the fundamental frequency (n) to the second harmonic (n₁) is 1 : 2.

Here, L = 3\(\cfrac{\lambda}{2}\)

\(\therefore\) Wavelength, λ = \(\cfrac{2L}{3}\) = \(\cfrac{2\times 30}{3}\) = 20 cm.

Data: T_1/2 = 272d = 272 × 24 × 60 × 60s = 2.35 × 10⁷ s,

A₀ = 2.0uCi = 2.0 × 10^-6 × 3.7 × 10¹⁰ = 7.4 × 10⁴ dis/s

t = 1 year = 3.156 × 10⁷ s

(a) T_1/2 = \(\cfrac{0.693}{\lambda}\) = = 0.693 \(\tau\)

 ∴ The mean lifetime for 

⁵⁷Co = T = \(\cfrac{T_{1/2}}{0.693}\) = \(\cfrac{2.35\times10^7}{0.693}\) = 3391 x 10⁷ s

The decay constant for ⁵⁷Co = λ = \(\frac{1}T\)

= \(\cfrac{1}{3.391\times10^7s}\)

= 2949 × 10^-8 s^-1

(b) A₀ = N₀ A 

∴ N₀ = \(\cfrac{A_0}{\lambda}\) = A₀\(\tau\)

= (7.4 × 10⁴ )(3.391 × 10⁷)

= 2.509 × 10¹² nuclei

This is the required number.

(c) A(t) = A0e\(^{-\lambda t}\) = 2e^{-(2.949 x 10\(^{-8}\)) (3.156 x 10\(^{7}\))}

= 2e^-0.9307 = 2/e^0.9307

Let x = e^0.9307 

∴ Iog e^x = 0.9307

∴ 2.303 log₁₀x =  0.9307

∴ log_10^x =  \(\cfrac{0.9307}{2.303}\) = 0.4041

∴ x = antilog 0.4041 = 2.536

∴ A(t) = \(\cfrac{2}{2.536}\) μCi = 0.7886 μCi

 (a) \(^{226}_{86}Ra\) \(\longrightarrow\)\(^4_2\alpha\) + \(^{222}_{86}Em\)

Em (Emanation) ≡ Rn (Radon) 

Here, α particle is emitted and radon is formed.

(b) \(^{19}_{8}O\) \(\longrightarrow\) \(\bar{e}\) + \(^{19}_{9}F\)

Here, \(\bar{e}\) ≡ \(^0_{-1}\beta\) is emitted and fluorine is formed.

(c) \(^{228}_{90}Th\) \(\longrightarrow\) \(^4_2\alpha\) + \(^{224}_{88}Ra\)

Here, α particle is emitted and radium is formed.

(d) \(^{12}_{7}N\) \(\longrightarrow\) \(^{12}_{6}C\) + \(^0_{1}\beta\)

\(^0_{1}\beta\) is e⁺ (positron)

Here, β⁺ is emItted and carbon is formed.

i. d-block elements are also known as transition elements. The long form of periodic table contains four series of transition elements, known as transition series.

ii. Four transition series are 3d, 4d, 5d and 6d series wherein orbitals of (n - 1)^th main shell gets filled.

a. The 3d series contains the elements from Sc (Z = 21) to Zn (Z = 30) belonging to the 4^th period.

b. The 4d series contains the elements from Y (Z = 39) to Cd (Z = 48) belonging to the 5^th period.

c. The 5d series begins with La (Z = 57) and contains elements from Hf (Z = 72) to Hg (Z = 80) belonging to the 6^th period.

d. The 6d series begins with Ac (Z = 89) and contains elements from Rf (Z = 104) to Uub (Z = 112) belonging to the 7^th period.

(i)The elements of first transition series show decreasing tendency to form divalent cation as we move left to right in the series. This trend is due to general increase in the first and second ionization energy. The greater stability of Mn²⁺ is due to half filled d⁵ configuration and that of zinc is due to d¹⁰ configuration. 

(ii) All metal except Sc from oxide of type MO which are basic. The highest oxidation number in all oxide, coincide with the group number and is attain in Sc₂O₃ to Mn₂O₇. Formation of oxoanions is due to high electro negativity and small size of oxygen atom.

i. The last electron in the f-block elements enters into (n-2) f-orbitals, i.e., inner to the penultimate energy level and they form a transition series within the transition series (d-block elements). Hence, the f-block elements are known as inner transition series. 

ii. There are two series of inner transition elements:

a. Lanthanoids (atomic number 58-71) 

b. Actinoids (atomic number 90-103).

61 : [Xe]⁵⁴ 4f⁵ 5d⁰ 6s²

91 : [Rn]⁸⁶ 5f² 6d¹ 7s²

101 : [Rn]⁸⁶ 5f¹³ 5d⁰ 7s²

109: [Rn]⁸⁶ 5f¹⁴ 6d⁷ 7s²

(i) Electronic configuration:

The general electronic configuration for lanthanoids is [Xe] ^0-14 5d ^0-1 6s² and that of actinoids is [Rn] 5f ^0-14 6d^0-1 7s². Unlike 4f orbitals, 5 f orbitals are not deeply buried and participate in bonding to a greater extent.

(ii) Oxidation states:

The principal oxidation states of lanthanoids is (+3). However sometimes we also encounter oxidation states of +2 and +4. This is because of extra stability of fully-filled and half filled orbitals. Actinoids exhibit a greater range of oxidation states. This is because the 5f, 6d and 7s levels are of comparable energies. Again, (+3) is the principal oxidation state for actinoids. Actinoids such as lanthanoids have more compounds in +3 state than in +4 state.

(iii) Atomic and ionic size: 

Similar to lanthanoids, actinoids also exhibit actinoid contraction over all decrease in atomic and ionic radii. The contraction is greater due to the poor shielding effect of 5f orbitals. Hence there is an unexpected in the atomic and ionic sizes of actionoids.

(iv) Chemical reactivity

In the lanthanoide series, the earlier members of the series are more reactive. They have reactivity that is comparable to Ca. With an increase in the atomic number, the lanthanides start behaving similar to Al. Actinoids, on the other hand, are highly reactive metals, especially when they are finely divided. When they are added to boiling water, they give a mixture of oxide and hydride. Actinoids combine with most of the non metals at moderate temperatures. Alkalies have no action on these actinoids. In case of acids, they are slightly affected by nitric acid (because of the -formation of a protective oxide layer).

Lanthanoids primarily show three oxidation states, +3 states is the most common. Lanthanoids display a limited number of oxidation states because the difference between the energies of 4f, 5d and 6s orbitals is quite large. On the other hand, the energy difference between the 5f, 6d and 7s orbitals is very less. Hence, actinoids display a large number of oxidation states. For example uranium and plutonium display +3, +4, +5 and +6 oxidation states while neptunium display +3, +4, +5 and +7. The most common oxidation state in case of actinoids is also +3.

(i) In 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 atoms are not involved in bonding. As a result, it can donate electrons and behave as a base.

On the other hand, in the case of a higher oxide of a transition metal, the metal atom has a high oxidation state. This means that the valence electrons are involved in bonding. As a result, it can accept electrons and behave as an acid. For example, Mn^IIO is basic and Mn^VIIO is acidic.

(ii) Oxygen and fluorine act as strong oxidising agents because of their high electronegativities and small sizes. Hence, they bring out the highest oxidation states from the transition metals. In other words, a transition metal exhibits oxidation states in oxides and fluorides. For example, in O₅F₆ and V₂O₅, the oxidation states of O₅ and V are +6 and respectively.

(iii) Oxygen is a strong oxidising agent due to its high electronegativity and small size so, oxoanions of a metal have the highest oxidation state. For example, in MnO₄^-, the oxidation state of Mn is +7.

It is a transformation of a substance into two or more substances by simultaneous oxidation and reduction. 

Cu⁺ in aqueous solution underoes disproportionation, i.e., 

2Cu⁺ (aq) → Cu²⁺(aq) + Cu(s) 

The E⁰ value for this is favourable.

The regular decrease in atomic radii due to the filling of 4f before 5d orbitals is called lanthanoid contraction. This is because of the imperfect shielding of one electron by another in the same set of orbitals. The shielding of one 4f electron by another is less than that of one d electron by another, and as the nuclear charge increases along the series, there is fairly regular decrease in the size of entire 4f orbitals. Consequences of lanthanoid contraction.

• Radii of third series are virtually same as those of the corresponding member of second series.
• Third series and second series have very similar physical and chemical properties much more than that expected by usual family relationships.

In the fast transition series, Cu exhibits +1 oxidation state very frequently. It is because Cu (+1) has an electronic configuration of [Ar] 3d¹⁰. The completely filled d - orbital makes it highly stable.

Vanadate : VO₃^-
Chromate : CrO₄^2-
Permanganate : MnO₄^-

Copper with configuration [Ar]3d¹⁰ electron 4s¹ exhibits +1 oxidation state. Copper loses 4s¹ electron easily and achieved a stable configuration 3d¹⁰ by forming Cu⁺.

From Sc to Mn the oxidation state leading to the maximum stability corresponding values of sum of 4s & 3d electrons. the element .

Example: In group 3, Sc forms [Sc(III)O₂] ^-, in group 4, Ti forms [Ti(IV)O₃]^{2- ,}in group 5, V forms [V (V)O₃] ^- etc.

E⁰ value of Cr²⁺ is more negative than the E⁰ value of Fe²⁺.

Potassium dichromate, in acidic medium acts as a strong oxidising agent by gaining 6e’ and forms Cr³⁺.
Cr₂O₇^2- + 14H⁺ + 6e^– → 2Cr³⁺ + 7H₂O   ..(1)

(i) iodides
6I^– → 3I₂ + 6e^– ..(2)
(1) + (2)
Cr₂O₇^2- + 14 H⁺ + 6I^– → 2Cr³⁺ + 3I₂ + 7H₂O

(ii) iron (II) solution
6Fe²⁺ → 6Fe³⁺ + 6e^– ..(3)
(1) + (3)
Cr₂O₇^2- +14H⁺+ 6Fe²⁺ → 2Cr³⁺ + 6Fe³⁺ + 7H₂O

(iii) H₂S
3H₂S → 6H⁺ + 3S + 6e^– ..(4)
(1) + (4)
Cr₂O₇^2- +14H⁺ + 3H₂S → 6H⁺ + 3S + 2Cr³⁺ + 7H₂O

Potassium Dichromates are generally prepared from chromates which in turn are obtained by the fusion of chromite ore (FeCr₂O₄) with sodium or potassium carbonate in free excess of air

4FeCr₂O₄ + 8Na₂CO₃ + 7O₂ → 8Na₂CrO₄ + 2Fe₂O₃ + 8CO₂

The yellow solution of Na₂CrO₄ is filtered and acidified with H₂SO₄ to give a solution from which orange sodium dichromate Na₂Cr₂O₇ 2H₂O can be crystallised
2Na₂CrO₄ + 2H⁺→ Na₂Cr₂O₇ + 2Na⁺ + H₂O

sodium dichromate is more soluble than potassium dichromate. The latter is prepared by treating the solution of Na₂Cr₂O₄ with KCl.

Na₂Cr₂O₇ + 2KCl → K₂Cr₂O₇ + 2NaCl (orange crystals)

(b) On increasing the PH of a solution of K₂Cr₂O₇, it behaves like a strong oxidising agent and it oxidises iodide to iodine sulphides to sulphur, tin (II) to tin (IV) and Iron (II) salts to iron (III).

The effect of Heisenberg uncertainty principle is significant only for motion of microscopic objects and is negligible for that of macroscopic objects. This can be explained by following example- If uncertainty principle is applied to an object of mass, say about a milligram (10^-6 kg).

∆_v.∆_x = \(\frac{h }{4π.m}\)

= \(\frac{6.626 \times 10^{−34}J s} {4 \times 3.1416 \times10^{−6}kg} =10^{−28}m^{2 }s^{−1}\)

∴ The value of ∆_v.∆_x obtained is extremely small and is insignificant. So, this principle has no significance in our everyday life.

No. significance as in daily life we deal with macro particles (large mass) & Δx.Δ ∝ 1/m so uncertainty in position of mass or velocity is least.

Selenium has two allotropic forms as follows :

(i) Red (non-metallic) form 

(ii) Grey (metallic) form

The thinning of the ozone layer in the upper atmosphere is called ozone depletion. This thinning has been more pronounced in the polar regions, especially over the Antarctica.

Option : (b) An allotropic oxygen

Uses of Ozone :

• Ozone sterilises drinking water by oxidising germs and bacteria present in it. 
• It is used as a bleaching agent for ivory, oils, starch, wax and delicate fabrics like silk. 
• Ozone is used to purify the air in crowded places like Clnema halls, railways, tunnels, etc. 
• In industry, ozone is used in the manufacture of synthetic camphor, potassium permanganate, etc. 

• The depletion of ozone layer increases the amount of ultraviolet radiation reaching the Earth. 
• This has caused an increase in the rate of skin cancer, eye cataracts and damage to the genetic as well as immune system. 
• Thus, ozone depletion has become a major environ-mental problem. 

(i) P₄ + 6Cl₂ → 4PCl₃ and P₄ + 10Cl₂ → 4PCl₅ 

(ii) 2As + 3Cl₂→ 2AsCl₃

(iii) 2Sb + 3Cl₂ → 2SbCl₃

(iv) 2B + 3Cl₂ → 2BCl₃ 

(v) S₈ + 4Cl₂ → 4S₂Cl₂

Sulphur monochloride.

(i) 2XeF₂ (s) + 2H₂O(l) → 2Xe (g) + 4 HF(aq) + O₂(g

(ii) 6XeF₄ + 12 H₂O → 4Xe + 2XeO₃ + 24 HF + 3O₂

(iii) XeF₆ + 3 H₂O → XeO₃ + 6 HF

Partial hydrolysis of XeF₆ gives oxyfluorides,

XeF₆ + H₂O → XeOF₄ + 2HF

XeF₆ + 2 H₂O → XeO₂F₂ + 4HF

Uses of neon (Ne) :

• Neon is used in the production of neon discharge lamps and signs by filling Ne in glass discharge tubes.
• Neon signs are visible from a long distance and also have high penetrating power in mist or fog.
• A mixture of neon and helium is used in voltage stabilizers and current rectifiers.
• Neon is also used in the production of lasers and fluorescent tubes.

 Uses of argon (Ar) :

• Argon is used to fill fluorescent tubes and radio valves.
• It is used to provide inert atmosphere for welding and production of steel.
• It is used along with neon in neon sign lamps to obtain different colours.
• A mixture of 85% Ar and 15% N₂ is used in electric bulbs to enhance the life of the filament.

• Preparation of XeO₃ : Xenon trioxide (XeO₃) is prepared by the hydrolysis of XeF₄ or XeF₆.
• By hydrolysis of XeF₄ : 3XeF₄ + 6H₂0 → 2Xe + XeO₃ + 12 HF + \(1\frac{1}{2}O_2\)
• By hydrolysis of XeF₆ : XeF₆ + 3H₂O → XeO₃ + 6HF
• Preparation of XeOF₄ : Xenon oxytetrafluoride (XeOF₄) is prepared by the partial hydrolysis of XeF₆.

XeF₆ + H₂O → XeOF₄ + 2HF

In agricultural practices, instead of fertilizers, manures should be commonly employed because the Continuous use of fertilizers in an area can destroy soil fertility as the organic matter in the soil is not replenished and it also affects various microorganisms present in the soil which are beneficial for maintaining soil quality.