Solve this following
Question: Evaluate: $\int(1-x) \sqrt{x} d x$ Ans. $\frac{2}{15} \mathrm{x} \sqrt{\mathrm{x}}(5-3 \mathrm{x})+\mathrm{C}$ Solution:...
Read More →Radioactive 131I has a half-life of 8.0 days.
Question: Radioactive ${ }^{131}$ I has a half-life of $8.0$ days. A sample containing ${ }^{131}$ I has activity $20 \mu$ Ci at $t=0$. (a) What is its activity at $t=4.0$ days? (b) What is its decay constant at $t=4.0$ days? Solution:...
Read More →The half-life of 108Au is 2.7 days. (a) Find the activity of a sample
Question: The half-life of ${ }^{108} \mathrm{Au}$ is $2.7$ days. (a) Find the activity of a sample containing $1.00 \mu \mathrm{g}$ of ${ }^{198} \mathrm{Au}$. (b) What will be the activity after 7 days? Take the atomic weight of ${ }^{198}$ Au to be $198 \mathrm{~g} / \mathrm{mol}$. Solution:...
Read More →Solve this following
Question: Evaluate: $\int \frac{\sin (x-\alpha)}{\sin (x+\alpha)} d x$ Ans. $x \cos 2 \alpha-\sin 2 \alpha \cdot \log |\sin (x+\alpha)|+C$ Solution:...
Read More →The decay constant of (electron capture to) is
Question: The decay constant of (electron capture to) is $1.8 \times 10^{-4} \gamma^{-1}$. (a) What is the half-life? (b) What is the average-life? (c) How much time will it take to convert $25 \%$ of this isotope of mercury into gold? Solution:...
Read More →Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:
Question: Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme: $12 \mathrm{~N} \rightarrow{ }^{12} \mathrm{C}^{*}+\mathrm{e}^{+}+\mathrm{V}$ ${ }^{12} \mathrm{C}^{*} \rightarrow{ }^{12} \mathrm{C}+\gamma(4.43 \mathrm{MeV})$ The atomic mass of ${ }^{12} \mathrm{~N}$ is $12.018613 \mathrm{u}$ Solution:...
Read More →228Th emits an alpha particle to reduce to 224Ra.
Question: ${ }^{228}$ Th emits an alpha particle to reduce to ${ }^{224} \mathrm{Ra}$. Calculate the kinetic energy of the alpha particle emitted in the following decay: ${ }^{228} \mathrm{Th} \rightarrow{ }^{224} \mathrm{Ra}{ }^{\star}+\alpha$ ${ }^{224} \mathrm{Ra}^{*} \rightarrow{ }^{224} \mathrm{Ra}+\gamma(217 \mathrm{keV})$ Atomic mass of ${ }^{228} \mathrm{Th}$ is $228.028726 \mathrm{u}$, that of ${ }^{224} \mathrm{Ra}$ is $224.020196 \mathrm{u}$ and that of ${ }^{4}{ }_{2} \mathrm{He}$ is...
Read More →The masses of
Question: The masses of ${ }^{11} \mathrm{C}$ and ${ }^{11} \mathrm{~B}$ are respectively $11.0114 \mathrm{u}$ and $11.0093 \mathrm{u}$. Find the maximum energy a positron can have in the $\beta^{+}$-decay of ${ }^{11} \mathrm{C}$ to ${ }^{11} \mathrm{~B}$. Solution:...
Read More →Solve this following
Question: Evaluate: $\int \frac{\cos (x+a)}{\sin (x+b)} d x$ Ans. $\cos (a-b) \log |\sin (x+b)|-x \sin (a-b)+C$ Solution:...
Read More →Lithium (Z=3) has two stable isotopes 6Li and 7Li.
Question: Lithium ( $\mathrm{Z}=3)$ has two stable isotopes ${ }^{6} \mathrm{Li}$ and ${ }^{7} \mathrm{Li}$. When neutrons are bombarded on lithium sample, electrons and $\alpha$ particles are ejected. Write down the nuclear processes taking place. Solution:...
Read More →Potassium -40 can decay in three modes.
Question: Potassium $-40$ can decay in three modes. It can decay by $\beta$-emission, $\beta^{+}$-emission or electron capture. (a) Write the equations showing the end products. (b) Find the Q-values in each of the three cases. Atomic masses of $1840 \mathrm{Ar}, 1940 \mathrm{~K}$ and $2040 \mathrm{Ca}$ are $39.9624 \mathrm{u}, 39.9640 \mathrm{u}$ and $39.9626 \mathrm{u}$ respectively. Solution:...
Read More →Solve this following
Question: Evaluate: $\int \frac{(1+\tan x)}{(1-\tan x)} d x$ Ans. $-\log |\cos x-\sin x|+C$ Solution: Given:...
Read More →Prove the following
Question: In the decay ${ }^{64} \mathrm{Cu} \rightarrow{ }^{64} \mathrm{Ni}+\mathrm{e}^{+}+\mathrm{v}$, the maximum kinetic energy carried by the position is found to be $0.650 \mathrm{MeV}$. (a) What is the energy of the neutrino which was emitted together with a positron of kinetic energy $0.150 \mathrm{MeV}$ ? (b) What is the momentum of this neutrino in $\mathrm{kg}-\mathrm{m} / 3$ ? Use the formula applicable to a photon. Solution:...
Read More →Solve this following
Question: Evaluate: $\int\left(\frac{1+\cos x}{1-\cos x}\right) d x$ Ans. $-2 \cot \frac{x}{2}-x+C$ Solution: $=-2 \cot \frac{x}{2}-x+c$...
Read More →Complete the following decay schemes.
Question: Complete the following decay schemes. (a) ${ }_{88}^{226} R a \rightarrow \alpha+{ }_{86}^{112} R n$ (b) ${ }_{8}^{19} \mathrm{O} \rightarrow{ }_{9}^{19} F+{ }_{-1} e^{0}$ (c) ${ }_{13}^{25} \mathrm{Al} \rightarrow{ }_{12}^{25} \mathrm{Mg}+{ }_{1} e^{0}$ Solution: (a) ${ }_{88}^{226} R a \rightarrow{ }_{2}^{4} \propto+{ }_{26}^{112} R n$ (b) ${ }_{8}^{19} O \rightarrow{ }_{9}^{19} F+{ }_{n}^{0} \beta+{ }_{0}^{0} \overline{\mathrm{v}}$ (c) ${ }_{13}^{25} \mathrm{Al} \rightarrow{ }_{12}^...
Read More →A free neutron beta-decays to a proton with a half-life of 14 minutes.
Question: A free neutron beta-decays to a proton with a half-life of 14 minutes. (a) What is the decay constant? (b) Find the energy liberated in the process. Solution:...
Read More →32P beta-decays to 32S. Find the sum of the energy of the antineutrino and
Question: ${ }^{32} \mathrm{P}$ beta-decays to ${ }^{32} \mathrm{~S}$. Find the sum of the energy of the antineutrino and the kinetic energy of the $\beta$ - particle. Neglect the recoil of the daughter nucleus. Atomic mass of ${ }^{32} \mathrm{P}=31.974 \mathrm{u}$ and that of ${ }^{32} \mathrm{~S}=31.972 \mathrm{u}$. Solution:...
Read More →Calculate the minimum energy needed to separate a neutron
Question: Calculate the minimum energy needed to separate a neutron from a nucleus with Z protons and $\mathrm{N}$ neutrons in terms of the masses $\mathrm{M}_{\mathrm{Z}, \mathrm{N}}, \mathrm{M}_{\mathrm{Z}, \mathrm{N}-1}$ and the mass of the neutron. Solution: Energy released $=($ Initial mass of nucleus-Final mass of nucleus $) \mathrm{C}^{2}$ $=\left(M_{Z . N-1}+M_{0}-M_{Z N}\right) C^{2}$...
Read More →Solve this following
Question: Evaluate: $\int \frac{d x}{(\sqrt{x+3}-\sqrt{x+2})}$ Ans. $\frac{2}{3}(x+3)^{3 / 2}+\frac{2}{3}(x+2)^{3 / 2}+C$ Solution:...
Read More →Show that the minimum energy needed to separate a proton from
Question: Show that the minimum energy needed to separate a proton from a nucleus with Z protons and $\mathrm{N}$ neutrons is $\Delta \mathrm{E}=\left(\mathrm{M}_{\mathrm{Z}-1, \mathrm{n}}+\mathrm{M}_{\mathrm{H}}-\mathrm{M}_{\mathrm{Z}, \mathrm{N}}\right) \mathrm{c}^{2}$ Where $M_{Z, N}=$ mass of an atom with $Z$ protons and $N$ neutrons in the nucleus and $M_{H}=$ mass of a hydrogen atom. This energy is known as proton-separation energy. Solution:...
Read More →Find the energy liberated are as follows:
Question: Find the energy liberated are as follows: 223Ra209Pb+14C The atomic masses needed are as follows: $\begin{array}{lll}{ }^{223} \mathrm{Ra} { }^{209} \mathrm{~Pb} { }^{14} \mathrm{C} \\ 223.018 \mathrm{u} 208.981 \mathrm{u} 14.003 \mathrm{u}\end{array}$ Solution:...
Read More →(a) Calculate the energy released if 238U emits an ????-particle.
Question: (a) Calculate the energy released if ${ }^{238} \mathrm{U}$ emits an $\alpha$-particle. (b) Calculate the energy to be supplied to ${ }^{238} \mathrm{U}$ if two protons and two neutrons are to be emitted one by one. The atomic masses of ${ }^{238} \mathrm{U},{ }^{234} \mathrm{Th}$ and ${ }^{4} \mathrm{He}$ are $238.0508 \mathrm{u}, 234.04363 \mathrm{u}$ and 4.00260u respectively. Solution:...
Read More →Find the binding energy per nucleon of
Question: Find the binding energy per nucleon of $79197 \mathrm{Au}$ if its atomic mass is $196.96 \mathrm{u}$. Solution:...
Read More →How much energy is released in the following reaction?
Question: How much energy is released in the following reaction? $7^{L i}+p \rightarrow \alpha+\alpha$ Atomic mass of $7 \mathrm{Li}=7.0160 \mathrm{u}$ and that of ${ }^{4} \mathrm{He}=4.0026 \mathrm{u}$. Solution:...
Read More →Calculate the mass of an α-particle.
Question: Calculate the mass ofan-particle. Its binding energy is 28.2MeV. Solution:...
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