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The wave function $$(\Psi)$$ of $$2s$$ is given by
$$\Psi_{2s} = \frac{1}{2\sqrt{2\pi}}\left(\frac{1}{a_0}\right)^{1/2}\left(2 - \frac{r}{a_0}\right)e^{-r/2a_0}$$
At $$r = r_0$$, radial node is formed. Thus, $$r_0$$ in terms of $$a_0$$
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Maximum number of electrons that can be accommodated in shell with $$n = 4$$ are:
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Bond dissociation energy of E $$-$$ H bond of the "H$$_2$$E" hydrides of group 16 elements (given below), follows order.
(A) O
(B) S
(C) Se
(D) Te
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Chlorides of which metal are soluble in organic solvents:
Which of the following reaction is correct?
Boric acid in solid, whereas BF$$_3$$ is gas at room temperature because of
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The most stable carbocation for the following is:
The correct order of pK$$_a$$ values for the following compounds is:
Match List I with List II:
| List I (Mixture) | List II (Separation Technique) |
|---|---|
| (A) CHCl$$_3$$ + C$$_6$$H$$_5$$NH$$_2$$ | I. Steam distillation |
| (B) C$$_6$$H$$_{14}$$ + C$$_5$$H$$_{12}$$ | II. Differential extraction |
| (C) C$$_6$$H$$_5$$NH$$_2$$ + H$$_2$$O | III. Distillation |
| (D) Organic compound in H$$_2$$O | IV. Fractional distillation |
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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A:
can be easily reduced using Zn $$-$$ Hg/HCl to
.
Reason R: Zn $$-$$ Hg/HCl is used to reduce carbonyl group to $$-$$CH$$_2-$$ group.
In the light of the above statements, choose the correct answer from the options given below:
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The water quality of a pond was analysed and its BOD was found to be 4. The pond has
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Given below are two statements:
Statement I: During Electrolytic refining, the pure metal is made to act as anode and its impure metallic form is used as cathode.
Statement II: During the Hall-Heroult electrolysis process, purified Al$$_2$$O$$_3$$ is mixed with Na$$_3$$AlF$$_6$$ to lower the melting point of the mixture.
In the light of the above statements, choose the most appropriate answer from the options given below:
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Formulae for Nessler's reagent is:
KMnO$$_4$$ oxidises I$$^-$$ in acidic and neutral/faintly alkaline solution, respectively to
Match List I with List II:
| List I (Complexes) | List II (Hybridisation) |
|---|---|
| (A) [Ni(CO)$$_4$$] | I. sp$$^3$$ |
| (B) [Cu(NH$$_3$$)$$_4$$]$$^{2+}$$ | II. dsp$$^2$$ |
| (C) [Fe(NH$$_3$$)$$_6$$]$$^{2+}$$ | III. sp$$^3$$d$$^2$$ |
| (D) [Fe(H$$_2$$O)$$_6$$]$$^{2+}$$ | IV. d$$^2$$sp$$^3$$ |
1 L, 0.02M solution of [Co(NH$$_3$$)$$_5$$ SO$$_4$$]Br is mixed with 1 L, 0.02M solution of [Co(NH$$_3$$)$$_5$$Br]SO$$_4$$. The resulting solution is divided into two equal parts (X) and treated with excess AgNO$$_3$$ solution and BaCl$$_2$$ solution respectively as shown below:
1 L Solution (X) + AgNO$$_3$$ solution (excess) $$\to$$ Y
1 L Solution (X) + BaCl$$_2$$ solution (excess) $$\to$$ Z
The number of moles of Y and Z respectively are
The Cl $$-$$ Co $$-$$ Cl bond angle values in a fac-[Co(NH$$_3$$)$$_3$$Cl$$_3$$] complex is/are:
Decreasing order towards S$$_N$$1 reaction for the following compounds is:
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Given below are two statements: One is labelled as Assertion A and the other labelled as Reason R.
Assertion A: Antihistamines do not affect the secretion of acid in stomach.
Reason R: Antiallergic and antacid drugs work on different receptors.
In the light of the above statements, choose the correct answer from the options given below:
1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $$27°$$C. The work done is $$3$$ kJ mol$$^{-1}$$. The final temperature of the gas is ______ K (Nearest integer). Given $$C_v = 20$$ J mol$$^{-1}$$ K$$^{-1}$$
Consider the following equation:
$$2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g), \Delta H = -190$$ kJ.
The number of factors which will increase the yield of SO$$_3$$ at equilibrium from the following is ______.
A. Increasing temperature
B. Increasing pressure
C. Adding more SO$$_2$$
D. Adding more O$$_2$$
E. Addition of catalyst
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The strength of $$50$$ volume solution of hydrogen peroxide is ______ g/L (Nearest integer).
Given: Molar mass of H$$_2$$O$$_2$$ is 34 g mol$$^{-1}$$. Molar volume of gas at STP = 22.7 L.
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Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of $$5.0$$ $$\text{\AA}$$. If density of the FeO in the crystal is $$4.0$$ g cm$$^{-3}$$, then the number of FeO units present per unit cell is ______ (Nearest integer)
Given: Molar mass of Fe and O is 56 and 16 g mol$$^{-1}$$ respectively.
N$$_A = 6.0 \times 10^{23}$$ mol$$^{-1}$$
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Lead storage battery contains $$38\%$$ by weight solution of H$$_2$$SO$$_4$$. The van't Hoff factor is $$2.67$$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ______ (Nearest integer).
Given K$$_f = 1.8$$ K kg mol$$^{-1}$$
The electrode potential of the following half cell at 298 K
X|X$$^{2+}$$(0.001M)||Y$$^{2+}$$(0.01M)|Y is ______ $$\times 10^{-2}$$ V (Nearest integer)
Given: E$$^0_{X^{2+}/X} = -2.36$$ V
E$$^0_{Y^{2+}/Y} = +0.36$$ V
$$\frac{2.303 RT}{F} = 0.06$$ V
An organic compound undergoes first order decomposition. If the time taken for the $$60\%$$ decomposition is $$540$$ s, then the time required for $$90\%$$ decomposition will be ______ s. (Nearest integer).
Given: $$\ln 10 = 2.3$$; $$\log 2 = 0.3$$
The graph of $$\log \frac{x}{m}$$ vs $$\log p$$ for an adsorption process is a straight line inclined at an angle of $$45°$$ with intercept equal to $$0.6020$$. The mass of gas adsorbed per unit mass of adsorbent at the pressure of $$0.4$$ atm is ______ $$\times 10^{-1}$$ (Nearest integer)
Given: $$\log 2 = 0.3010$$
Number of compounds from the following which will not dissolve in cold NaHCO$$_3$$ and NaOH solutions but will dissolve in hot NaOH solution is ______.
A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of leucine (L) and two moles of valine (V) per mole of peptide. The number of peptide linkages in it are ______.
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