Write down the reactions involved during the formation of photochemical smog.
Question: Write down the reactions involved during the formation of photochemical smog. Solution: Photochemical smog is formed as a result of the reaction of sunlight with hydrocarbons and nitrogen oxides. Ozone, nitric oxide, acrolein, formaldehyde, and peroxyacetyl nitrate (PAN) are common components of photochemical smog. The formation of photochemical smog can be summarized as follows: Burning of fossil fuels leads to the emission of hydrocarbons and nitrogen dioxide in the atmosphere. High ...
Read More →If a, b, c are in A.P,; b, c, d are in G.P and are in A.P. prove that a, c, e are in G.P.
Question: If $a, b, c$ are in A.P, $, b, c, d$ are in G.P and $\frac{1}{c}, \frac{1}{d}, \frac{1}{e}$ are in A.P. prove that $a, c, e$ are in G.P. Solution: It is aiven that $a \cdot b \cdot c$ are in A.P. $\therefore b-a=c-b \ldots(1)$ It is given that $b, c, d$, are in G.P. $\therefore c^{2}=b d \ldots(2)$ Also, $\frac{1}{c}, \frac{1}{d}, \frac{1}{c}$ are in A.P. $\frac{1}{d}-\frac{1}{c}=\frac{1}{e}-\frac{1}{d}$ $\frac{2}{d}=\frac{1}{c}+\frac{1}{e}$ (3) It has to be proved that $a, c, e$ are i...
Read More →Examine the following functions for continuity.
Question: (a) $f(x)=x-5$ (b) $f(x)=\frac{1}{x-5}, x \neq 5$ (c) $f(x)=\frac{x^{2}-25}{x+5}, x \neq-5$ (d) $f(x)=|x-5|$ Solution: (a) The given function is It isevident thatfis defined at every real numberkand its value atkisk 5. It is also observed that, $\lim _{x \rightarrow k} f(x)=\lim _{x \rightarrow k}(x-5)=k-5=f(k)$ $\therefore \lim _{x \rightarrow k} f(x)=f(k)$ Hence,fis continuous at every real number and therefore, it is a continuous function. (b) The given function is $f(x)=\frac{1}{x-...
Read More →What is smog? How is classical smog different from photochemical smog?
Question: What is smog? How is classical smog different from photochemical smog? Solution: Smog is a kind of air pollution. It isthe blend of smoke and fog. There are two kinds of smog: a) Classical smog b) Photochemical smog The two smogs can be differentiated as follows:...
Read More →Statues and monuments in India are affected by acid rain.
Question: Statues and monuments in India are affected by acid rain. How? Solution: Acid rainis a byproduct of various human activities that leads to the emission of oxides of sulphur and nitrogen in the atmosphere. These oxides undergo oxidation and then react with water vapour to form acids. $2 \mathrm{SO}_{2(g)}+\mathrm{O}_{2(g)}+2 \mathrm{H}_{2} \mathrm{O}_{(t)} \longrightarrow 2 \mathrm{H}_{2} \mathrm{SO}_{4(a q)}$ $4 \mathrm{NO}_{2(g)}+\mathrm{O}_{2(g)}+2 \mathrm{H}_{2} \mathrm{O}_{(t)} \lo...
Read More →The ratio of the A.M and G.M. of two positive numbers a and b,
Question: The ratio of the A.M and G.M. of two positive numbersaandb, ism:n. Show that$a: b=\left(m+\sqrt{m^{2}-n^{2}}\right):\left(m-\sqrt{m^{2}-n^{2}}\right)$ Solution: Let the two numbers beaandb. A.M $=\frac{a+b}{2}$ and G.M. $=\sqrt{a b}$ According to the given condition, $\frac{a+b}{2 \sqrt{a b}}=\frac{m}{n}$ $\Rightarrow \frac{(a+b)^{2}}{4(a b)}=\frac{m^{2}}{n^{2}}$ $\Rightarrow(a+b)^{2}=\frac{4 a b m^{2}}{n^{2}}$ $\Rightarrow(a+b)=\frac{2 \sqrt{a b} m}{n}$ $\ldots(1)$ Using this in the i...
Read More →Write nuclear reaction equations for
Question: (i) $\alpha$-decay of ${ }_{88}^{226} \mathrm{Ra}$ (ii) $\alpha$-decay of ${ }_{94}^{242} \mathrm{Pu}$ (iii) $\beta^{-}$-decay of ${ }_{15}^{32} \mathrm{P}$ (iv) $\beta^{-}$-decay of ${ }_{83}^{210} \mathrm{Bi}$ (v) $\beta^{+}$-decay of ${ }_{6}^{11} \mathrm{C}$ (vi) $\beta^{+}$-decay of ${ }_{43}^{97} \mathrm{Tc}$ (vii) Electron capture of ${ }_{54}^{120} \mathrm{Xe}$ Solution: $\alpha$ is a nucleus of helium $\left({ }_{2} \mathrm{He}^{4}\right)$ and $\beta$ is an electron $\left(e^{...
Read More →Examine the continuity of the function.
Question: Examine the continuity of the function $f(x)=2 x^{2}-1$ at $x=3$. Solution: The given function is $f(x)=2 x^{2}-1$ At $x=3, f(x)=f(3)=2 \times 3^{2}-1=17$ $\lim _{x \rightarrow 3} f(x)=\lim _{x \rightarrow 3}\left(2 x^{2}-1\right)=2 \times 3^{2}-1=17$ $\therefore \lim _{x \rightarrow 3} f(x)=f(3)$ Thus,fis continuous atx= 3...
Read More →If a and b are the roots of are roots of ,
Question: If $a$ and $b$ are the roots of $x^{2}-3 x+p=0$ and $c, d$ are roots of $x^{2}-12 x+q=0$, where $a, b, c, d$, form a G.P. Prove that $(q+p):(q-p)=17: 15$. Solution: It is given that $a$ and $b$ are the roots of $x^{2}-3 x+p=0$ $\therefore a+b=3$ and $a b=p \ldots$ (1) Also, $c$ and $d$ are the roots of $x^{2}-12 x+q=0$ $\therefore c+d=12$ and $c d=q \ldots$ (2) It is given that $a, b, c, d$ are in G.P. Let $a=x, b=x r, c=x r^{2}, d=x r^{3}$ From (1) and (2), we obtain $x+x r=3$ $\Right...
Read More →A given coin has a mass of 3.0 g.
Question: A given coin has a mass of $3.0 \mathrm{~g}$. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of ${ }_{29}^{63} \mathrm{Cu}$ atoms (of mass $62.92960 \mathrm{u}$ ). Solution: Mass of acopper coin,m = 3 g Atomic mass of ${ }_{29} \mathrm{Cu}^{63}$ atom, $m=62.92960 \mathrm{u}$ The total number of ${ }_{29} \mathrm{Cu}^{63}$ atoms in the coin, $N=\frac{N_{\mathrm{A}} \times ...
Read More →Prove that the functionis continuous at
Question: Prove that the function $f(x)=5 x-3$ is continuous at $x=0$, at $x=-3$ and at $x=5$. Solution: The given function is $f(x)=5 x-3$ At $x=0, f(0)=5 \times 0-3=-3$ $\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0}(5 x-3)=5 \times 0-3=-3$ $\therefore \lim _{x \rightarrow 0} f(x)=f(0)$ Therefore,fis continuous atx= 0 At $x=-3, f(-3)=5 \times(-3)-3=-18$ $\lim _{x \rightarrow-3} f(x)=\lim _{x \rightarrow-3}(5 x-3)=5 \times(-3)-3=-18$ $\therefore \lim _{x \rightarrow-3} f(x)=f(-3)$ herefor...
Read More →Obtain the binding energy of the nuclei
Question: Obtain the binding energy of the nuclei ${ }_{26}^{56} \mathrm{Fe}$ and ${ }_{83}^{209} \mathrm{Bi}$ in units of $\mathrm{MeV}$ from the following data: $m\left({ }_{26}^{56} \mathrm{Fe}\right)=55.934939 \mathrm{u} m\left({ }_{83}^{209} \mathrm{Bi}\right)=208.980388 \mathrm{u}$ Solution: Atomic mass of ${ }_{26}^{56} \mathrm{Fe}, m_{1}=55.934939 \mathrm{u}$ ${ }_{26}^{56} \mathrm{Fe}$ nucleus has 26 protons and $(56-26)=30$ neutrons Where, Mass ofa proton,mH= 1.007825 u Mass of a neutr...
Read More →If a, b, c, d are in G.P, prove that are in G.P.
Question: If $a, b, c, d$ are in G.P, prove that $\left(a^{n}+b^{n}\right),\left(b^{n}+c^{n}\right),\left(c^{n}+d^{n}\right)$ are in G.P. Solution: It is given thata,b,c,anddare in G.P. $\therefore b^{2}=a c \ldots(1)$ $c^{2}=b d \ldots(2)$ $a d=b c \ldots(3)$ It has to be proved that $\left(a^{n}+b^{n}\right),\left(b^{n}+c^{n}\right),\left(c^{n}+d^{n}\right)$ are in G.P. i.e., $\left(b^{n}+c^{n}\right)^{2}=\left(a^{n}+b^{n}\right)\left(c^{n}+d^{n}\right)$ Consider L.H.S. $\left(b^{n}+c^{n}\righ...
Read More →Obtain the binding energy (in MeV) of a nitrogen nucleus
Question: Obtain the binding energy (in MeV) of a nitrogen nucleus $\left({ }_{7}^{14} \mathrm{~N}\right)$, given $m\left({ }_{7}^{14} \mathrm{~N}\right)=14.00307 \mathrm{u}$ Solution: Atomic mass of nitrogen $\left({ }_{7} \mathrm{~N}^{14}\right), m=14.00307 \mathrm{u}$ A nucleus of nitrogen ${ }_{7} \mathrm{~N}^{14}$ contains 7 protons and 7 neutrons. Hence,the mass defect of this nucleus, Δm= 7mH+ 7mnm Where, Mass ofa proton,mH= 1.007825 u Mass of a neutron,mn= 1.008665 u Δm= 7 1.007825 + 7 1...
Read More →List gases which are responsible for greenhouse effect.
Question: List gases which are responsible for greenhouse effect. Solution: The major greenhouse gases are: 1) Carbon dioxide (CO2) 2) Methane (CH4) 3) Water (H2O) 4) Nitrous oxide (NO) 5) Ozone (O3) 6) Chlorofluorocarbons (CFCs)...
Read More →The three stable isotopes of neon:
Question: The three stable isotopes of neon: ${ }_{10}^{20} \mathrm{Ne},{ }_{10}^{21} \mathrm{Ne}$ and ${ }_{10}^{22} \mathrm{Ne}$ have respective abundances of $90.51 \%, 0.27 \%$ and $9.22 \%$. The atomic masses of the three isotopes are $19.99 \mathrm{u}, 20.99 \mathrm{u}$ and $21.99 \mathrm{u}$, respectively. Obtain the average atomic mass of neon. Solution: Atomic mass of ${ }_{10}^{20} \mathrm{Ne}, m_{1}=19.99 \mathrm{u}$ Abundance of ${ }_{10}^{20} \mathrm{Ne}, \eta_{1}=90.51 \%$ Atomic m...
Read More →Carbon monoxide gas is more dangerous than carbon dioxide gas.
Question: Carbon monoxide gas is more dangerous than carbon dioxide gas. Why? Solution: Carbon dioxide (CO2) and carbon monoxide (CO) gases are emitted during the combustion of various fuels. Carbon monoxide is poisonous, whereas carbon-dioxide is non-toxic in nature. Carbon monoxide is poisonous because it is capable of forming a complex with haemoglobin (carboxyhaemoglobin), which is more stable than the oxygen-haemoglobin complex. The concentration range of 34% of carboxyhaemoglobin decreases...
Read More →Choose the correct answer.
Question: Choose the correct answer. Let $A=\left[\begin{array}{ccc}1 \sin \theta 1 \\ -\sin \theta 1 \sin \theta \\ -1 -\sin \theta 1\end{array}\right]$, where $0 \leq \theta \leq 2 \pi$, then A. $\operatorname{Det}(A)=0$ B. $\operatorname{Det}(\mathrm{A}) \in\left(2,^{\infty}\right)$ C. $\operatorname{Det}(A) \in(2,4)$ D. Det $(\mathrm{A}) \in[2,4]$ Solution: Answer: D $A=\left[\begin{array}{ccc}1 \sin \theta 1 \\ -\sin \theta 1 \sin \theta \\ -1 -\sin \theta 1\end{array}\right]$ $\therefore|A...
Read More →Two stable isotopes of lithium
Question: (a) Two stable isotopes of lithium ${ }_{3}^{6} \mathrm{Li}$ and ${ }_{3}^{7} \mathrm{Li}$ have respective abundances of $7.5 \%$ and $92.5 \%$. These isotopes have masses $6.01512 \mathrm{u}$ and $7.01600 \mathrm{u}$, respectively. Find the atomic mass of lithium. (b) Boron has two stable isotopes, ${ }_{5}^{10} \mathrm{~B}$ and ${ }_{5}^{11} \mathrm{~B}$. Their respective masses are $10.01294 \mathrm{u}$ and $11.00931 \mathrm{u}$, and the atomic mass of boron is $10.811 \mathrm{u}$. ...
Read More →Explain tropospheric pollution in 100 words.
Question: Explain tropospheric pollution in 100 words. Solution: Tropospheric pollution arises due to the presence ofundesirable substances in the lowest layer of the atmosphere. Oxides of sulphur, nitrogen, carbon, and hydrocarbons are the major gaseous pollutants. Oxides of sulphur (SO2and SO3) and nitrogen (NO2, NO) are produced as a result of burning of fossil fuels (coal, automobile fuel). These oxides react with water in the presence of atmospheric oxygen to form nitric acid (HNO3) and sul...
Read More →Choose the correct answer. If x, y, z are nonzero real numbers,
Question: Choose the correct answer. If $x, y, z$ are nonzero real numbers, then the inverse of matrix $A=\left[\begin{array}{lll}x 0 0 \\ 0 y 0 \\ 0 0 z\end{array}\right]$ is A. $\left[\begin{array}{lll}x^{-1} 0 0 \\ 0 y^{-1} 0 \\ 0 0 z^{-1}\end{array}\right]$ B. $x y z\left[\begin{array}{lll}x^{-1} 0 0 \\ 0 y^{-1} 0 \\ 0 0 z^{-1}\end{array}\right]$ C. $\frac{1}{x y z}\left[\begin{array}{lll}x 0 0 \\ 0 y 0 \\ 0 0 z\end{array}\right]$ D. $\frac{1}{x y z}\left[\begin{array}{lll}1 0 0 \\ 0 1 0 \\ ...
Read More →Define environmental chemistry.
Question: Define environmental chemistry. Solution: Environmental chemistry is the study of chemical and biochemical processes occurring in nature. It deals with the study of origin, transport, reaction, effects, and fates of various chemical species in the environment....
Read More →Why is Wurtz reaction not preferred for the preparation of alkanes containing odd number of carbon atoms?
Question: Why is Wurtz reaction not preferred for the preparation of alkanes containing odd number of carbon atoms? Illustrate your answer by taking one example. Solution: Wurtz reaction is limited for the synthesis of symmetrical alkanes (alkanes with an even number of carbon atoms) In the reaction, two similar alkyl halides are taken as reactants and an alkane, containing double the number of carbon atoms, are formed. Example: Wurtz reaction cannot be used for the preparation of unsymmetrical ...
Read More →Choose the correct answer. If a, b, c, are in A.P., then the determinant
Question: Choose the correct answer. Ifa,b,c, are in A.P., then the determinant $\left|\begin{array}{lll}x+2 x+3 x+2 a \\ x+3 x+4 x+2 b \\ x+4 x+5 x+2 c\end{array}\right|$ A. 0 B. 1 C. $x$ D. $2 x$ Solution: Answer:A $\begin{aligned} \Delta =\left|\begin{array}{lll}x+2 x+3 x+2 a \\ x+3 x+4 x+2 b \\ x+4 x+5 x+2 c\end{array}\right| \\ =\left|\begin{array}{lll}x+2 x+3 x+2 a \\ x+3 x+4 x+(a+c) \\ x+4 x+5 x+2 c\end{array}\right| \quad(2 b=a+c \text { as } a, b, \text { and } c \text { are in A.P. }) ...
Read More →Suggest the name of a Lewis acid other than anhydrous aluminium chloride which can be used during ethylation of benzene.
Question: Suggest the name of a Lewis acid other than anhydrous aluminium chloride which can be used during ethylation of benzene. Solution: The ethylation reaction of benzene involves the addition of an ethyl group on the benzene ring. Such a reaction is called a Friedel-Craft alkylation reaction. This reaction takes place in the presence of a Lewis acid. Any Lewis acid like anhydrous FeCl3, SnCl4, BF3etc. can be used during the ethylation of benzene....
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