From the relation R
Question: From the relationR=R0A1/3, whereR0is a constant andAis the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent ofA). Solution: We have the expression for nuclear radius as: R=R0A1/3 Where, R0= Constant. A= Mass number of the nucleus Nuclear matter density, $\rho=\frac{\text { Mass of the nucleus }}{\text { Volume of the nucleus }}$ Letmbe the average mass of the nucleus. Hence, mass of the nucleus =mA $\therefore \rho=\frac{m A}{\frac{4}{...
Read More →A large number of fish are suddenly found floating dead on a lake.
Question: A large number of fish are suddenly found floating dead on a lake. There is no evidence of toxic dumping but you find an abundance of phytoplankton. Suggest a reason for the fish kill. Solution: The amount of dissolved oxygen present in water is limited. The abundance of phytoplanktons causes depletion of this dissolved oxygen. This is because, phytoplanktons are degraded by bacteria present in water. For their decomposition, they require a large amount of oxygen. Hence, they consume t...
Read More →Calculate the height of the potential barrier for a head on collision of two deuterons.
Question: Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.) Solution: When two deuterons collide head-on, the distance between their centres,dis given as: Radius of 1stdeuteron + Radius of 2nddeuteron Radius of a deuteron nucleus = 2 fm = 21015m d= 21015+ 21015...
Read More →Calculate the height of the potential barrier for a head on collision of two deuterons.
Question: Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.) Solution: When two deuterons collide head-on, the distance between their centres,dis given as: Radius of 1stdeuteron + Radius of 2nddeuteron Radius of a deuteron nucleus = 2 fm = 21015m d= 21015+ 21015...
Read More →Shamshad Ali buys a scooter for Rs 22000.
Question: Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him? Solution: It is given that Shamshad Ali buys a scooter for Rs 22000 and pays Rs 4000 in cash. $\therefore$ Unpaid amount $=$ Rs $22000-$ Rs $4000=$ Rs 18000 According to the given condition, the interest paid annually is $10 \%$ of $18000,10 \%$ of $17000,10 \%$ of $16000 \ldots 10 \%$ o...
Read More →What would have happened if the greenhouse gases were totally missing in the earth’s atmosphere?
Question: What would have happened if the greenhouse gases were totally missing in the earths atmosphere? Discuss. Solution: Earth's most abundant greenhouse gases are $\mathrm{CO}_{2}, \mathrm{CH}_{4}, \mathrm{O}_{3}, \mathrm{CFCs}$, and water vapour. These gases are present near the Earth's surface. They absorb solar energy that is radiated back from the surface of the Earth. The absorption of radiation results in the heating up of the atmosphere. Hence, greenhouse gases are essential for main...
Read More →Find all points of discontinuity of f, where f is defined by
Question: Find all points of discontinuity off, wherefis defined by $f(x)=\left\{\begin{array}{l}x^{3}-3, \text { if } x \leq 2 \\ x^{2}+1, \text { if } x2\end{array}\right.$ Solution: The given function $f$ is $f(x)=\left\{\begin{array}{l}x^{3}-3, \text { if } x \leq 2 \\ x^{2}+1, \text { if } x2\end{array}\right.$ Thegiven functionfis defined at all the points of the real line. Letcbe a point on the real line. Case I: If $c2$, then $f(c)=c^{3}-3$ and $\lim _{x \rightarrow c} f(x)=\lim _{x \rig...
Read More →How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium?
Question: How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{1}^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ Solution: The given fusion reaction is: ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ Amount of deuterium,m= 2 kg 1 mole, i.e., 2 g of deuterium contains 6.0231023atoms. $\therefore 2.0 \m...
Read More →What do you mean by green chemistry?
Question: What do you mean by green chemistry? How will it help decrease environmental pollution? Solution: Green chemistry is a production processthat aims at using the existing knowledge and principles of chemistry for developing and implementing chemical products and processes to reduce the use and generation of substances hazardous to the environment The release of different harmful chemicals(particulates, gases, organic and inorganic wastes) causes environmental pollution. In green chemistr...
Read More →How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium?
Question: How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{1}^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ Solution: The given fusion reaction is: \${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ Amount of deuterium,m= 2 kg 1 mole, i.e., 2 g of deuterium contains 6.0231023atoms. $\therefore 2.0 \...
Read More →How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium?
Question: How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{1}^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ Solution: The given fusion reaction is: \${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ Amount of deuterium,m= 2 kg 1 mole, i.e., 2 g of deuterium contains 6.0231023atoms. $\therefore 2.0 \...
Read More →What are pesticides and herbicides?
Question: What are pesticides and herbicides? Explain giving examples. Solution: Pesticides are a mixture of two or more substances. They are used for killing pests. Pests include insects, plant pathogens, weeds, mollusks, etc., that destroy the plant crop and spread diseases. Aldrin and dieldrin are the names of some common pesticides Herbicides are pesticides specially meant for killing weeds. For example, sodium chlorate (NAClO3), sodium arsenite (Na3AsO3), etc....
Read More →Do you observe any soil pollution in your neighbourhood?
Question: Do you observe any soil pollution in your neighbourhood? What efforts will you make for controlling the soil pollution? Solution: Major sources of soil pollution are industrial wastes and agricultural pollutants such as pesticides, fertilizers, etc. It is very important to maintain the quality and fertility of soil to ensure and sustain the growth of plants and food crops. Insecticides like DDT are not soluble in water. For this reason, they remain in soil for a long time, contaminatin...
Read More →Find all points of discontinuity of f, where f is defined by
Question: Find all points of discontinuity off, wherefis defined by $f(x)=\left\{\begin{array}{l}x+1, \text { if } x \geq 1 \\ x^{2}+1, \text { if } x1\end{array}\right.$ Solution: The given function $f$ is $f(x)=\left\{\begin{array}{l}x+1, \text { if } x \geq 1 \\ x^{2}+1, \text { if } x1\end{array}\right.$ Thegiven functionfis defined at all the points of the real line. Letcbe a point on the real line. Case I: If $c1$, then $f(c)=c^{2}+1$ and $\lim _{x \rightarrow c} f(x)=\lim _{x \rightarrow ...
Read More →A farmer buys a used tractor for Rs 12000.
Question: A farmer buys a used tractor for Rs 12000 . He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus $12 \%$ interest on the unpaid amount. How much will be the tractor cost him? Solution: It is given that the farmer pays Rs 6000 in cash. Therefore, unpaid amount = Rs 12000 Rs 6000 = Rs 6000 According to the given condition, the interest paid annually is $12 \%$ of $6000,12 \%$ of $5500,12 \%$ of $5000, \ldots, 12 \%$ of 500 Thus, total interest to be pa...
Read More →What do you mean by Biochemical Oxygen Demand (BOD)?
Question: What do you mean by Biochemical Oxygen Demand (BOD)? Solution: Biochemical oxygen demand is the amount of oxygen requiredby bacteria to decompose organic matter in a certain volume of sample of water. Clean water would have a BOD value of less than 5 ppm, whereas highly polluted water has a BOD value of 17 ppm or more....
Read More →A 1000 MW fission reactor consumes half of its fuel in 5.00 y.
Question: A $1000 \mathrm{MW}$ fission reactor consumes half of its fuel in $5.00 \mathrm{y}$. How much ${ }_{92}^{235} \mathrm{U}$ did it contain initially? Assume that the reactor operates $80 \%$ of the time, that all the energy generated arises from the fission of ${ }_{92}^{235} \mathrm{U}$ and that this nuclide is consumed only by the fission process. Solution: Half life of the fuel of the fission reactor, $t_{\frac{1}{2}}=5$ years = 5 365 24 60 60 s We know that in the fission of $1 \math...
Read More →Have you ever observed any water pollution in your area?
Question: Have you ever observed any water pollution in your area? What measures would you suggest to control it? Solution: Water pollution arises as a result of various human activities. This includes discharges from wastewater treatment plants, run-off from agricultural fields, storm-water drainage, etc. Pollutants from these sources enter the water bodies, thereby contaminating the water and rendering it impure. Industries and chemical factories discharge toxic, heavy metals such as Fe, Mn, A...
Read More →Show that
Question: Show that $\frac{1 \times 2^{2}+2 \times 3^{2}+\ldots+n \times(n+1)^{2}}{1^{2} \times 2+2^{2} \times 3+\ldots+n^{2} \times(n+1)}=\frac{3 n+5}{3 n+1}$ Solution: $n^{\text {th }}$ term of the numerator $=n(n+1)^{2}=n^{3}+2 n^{2}+n$ $n^{\text {th }}$ term of the denominator $=n^{2}(n+1)=n^{3}+n^{2}$ $\frac{1 \times 2^{2}+2 \times 3^{2}+\ldots .+n \times(n+1)^{2}}{1^{2} \times 2+2^{2} \times 3+\ldots .+n^{2} \times(n+1)}=\frac{\sum_{K=1}^{n} a_{K}}{\sum_{K=1}^{n} a_{K}}=\frac{\sum_{K=1}^{n...
Read More →The fission properties of
Question: The fission properties of ${ }_{94}^{239} \mathrm{Pu}$ are very similar to those of ${ }_{92}^{235} \mathrm{U}$. The average energy released per fission is $180 \mathrm{MeV}$. How much energy, in MeV, is released if all the atoms in $1 \mathrm{~kg}$ of pure ${ }_{94}^{239} \mathrm{Pu}$ undergo fission? Solution: Average energy released per fission of ${ }_{94}^{239} \mathrm{Pu}, E_{a v}=180 \mathrm{MeV}$ Amount of pure $_{94} \mathrm{Pu}^{239}, m=1 \mathrm{~kg}=1000 \mathrm{~g}$ $N_{A}...
Read More →What are the major causes of water pollution?
Question: What are the major causes of water pollution? Explain. Solution: Water pollution arisesas a result of several human activities, which leads to the presence of several undesirable substances in water. Major water pollutants with their sources have been tabulated as follows: Rolesplayed by major pollutants are: 1.Pathogens:These water pollutants include bacteria and other organisms. They enter water from animal excreta and domestic sewage. Bacteria present in human excreta (for example,E...
Read More →Find all points of discontinuity of f, where f is defined by
Question: Find all points of discontinuity off, wherefis defined by $f(x)=\left\{\begin{array}{l}\frac{x}{|x|}, \text { if } x0 \\ -1, \text { if } x \geq 0\end{array}\right.$ Solution: The given function $f$ is $f(x)=\left\{\begin{array}{l}\frac{x}{|x|}, \text { if } x0 \\ -1, \text { if } x \geq 0\end{array}\right.$ It is known that, $x0 \Rightarrow|x|=-x$ Therefore, the given function can be rewritten as $f(x)=\left\{\begin{array}{l}\frac{x}{|x|}=\frac{x}{-x}=-1, \text { if } x0 \\ -1, \text ...
Read More →Suppose, we think of fission of a
Question: Suppose, we think of fission of a ${ }_{26}^{56} \mathrm{Fe}$ nucleus into two equal fragments, ${ }_{13}^{28} \mathrm{Al}$. Is the fission energetically possible? Argue by working out $Q$ of the process. Given $m\left({ }_{26}^{56} \mathrm{Fe}\right)=55.93494$ u and $m\left({ }_{13}^{28} \mathrm{Al}\right)=27.98191 \mathrm{u}$. Solution: The fission of ${ }_{26}^{56} \mathrm{Fe}$ can be given as: ${ }_{13}^{56} \mathrm{Fe} \longrightarrow 2{ }_{13}^{28} \mathrm{Al}$ It is given that: ...
Read More →Suppose, we think of fission of a
Question: Suppose, we think of fission of a ${ }_{26}^{56} \mathrm{Fe}$ nucleus into two equal fragments, ${ }_{13}^{28} \mathrm{Al}$. Is the fission energetically possible? Argue by working out $Q$ of the process. Given $m\left({ }_{26}^{56} \mathrm{Fe}\right)=55.93494$ u and $m\left({ }_{13}^{28} \mathrm{Al}\right)=27.98191 \mathrm{u}$. Solution: The fission of ${ }_{26}^{56} \mathrm{Fe}$ can be given as: ${ }_{13}^{56} \mathrm{Fe} \longrightarrow 2{ }_{13}^{28} \mathrm{Al}$ It is given that: ...
Read More →What do you mean by ozone hole?
Question: What do you mean by ozone hole? What are its consequences? Solution: In Polar regions, stratospheric clouds provide the surface for chlorine nitrate and hypochlorous acid, which react further to give molecular chlorine. Molecular chlorine and HOCl arephotolysed to give chlorine-free radicals. $\mathrm{ClONO}_{2(g)}+\mathrm{H}_{2} \mathrm{O}_{(g)} \longrightarrow \mathrm{HOCl}_{(g)}+\mathrm{HNO}_{3(g)}$ $\mathrm{ClONO}_{2(g)}+\mathrm{HCl}_{(g)} \longrightarrow \mathrm{Cl}_{2(g)}+\mathrm...
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