80197Hg decays to 79197Au through electron capture with a decay constant of 0.257 per day.
Question: $80197 \mathrm{Hg}$ decays to 79197Au through electron capture with a decay constant of $0.257$ per day. (a) What other particle or particles are emitted in the decay? (b) assume that the electron is captured from the $\mathrm{K}$ shell. Use moseley's law Solution:...
Read More →The half-life of 40K is 1.3×109y.
Question: The half-life of ${ }^{40} \mathrm{~K}$ is $1.3 \times 10^{9} \mathrm{y}$. A sample of $1.00 \mathrm{~g}$ of pure $\mathrm{KCL}$ fives $160 \mathrm{counts} / \mathrm{s}$. Calculate the relative abundance of $40 \mathrm{~K}$ (fraction of ${ }^{40} \mathrm{~K}$ present) in natural potassium. Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int 3^{x} d x=?$ A. $3^{\mathrm{x}}(\log 3)+\mathrm{C}$ B. $3^{x}+C$ C. $\frac{3^{x}}{\log 3}+C$ D. $\frac{\log 3}{3^{x}}+C$ Solution:...
Read More →The count rate of nuclear radiation coming from a radioactive sample containing
Question: The count rate of nuclear radiation coming from a radioactive sample containing ${ }^{128}$ I varies with time as follows. (a) Plot In ( $R_{0} / R$ ) against t. (b) from the slope of the best straight line through the points, find the decay constant $\lambda$. (c) Calculate the half-life $t_{1 / 2}$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt[3]{x^{2}} d x=?$ A. $\frac{5}{3} \mathrm{x}^{5 / 3}+\mathrm{C}$ B. $\frac{3}{5} \mathrm{x}^{5 / 3}+C$ C. $\frac{5}{3} \mathrm{x}^{3 / 5}+C$ D. $\frac{3}{5} \mathrm{x}^{3 / 5}+C$ Solution:...
Read More →Natural water contains a small amount of tritium (13H).
Question: Natural water contains a small amount of tritium (13H). This isotope beta-decay with a half-life of $12.5$ years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottle of whisky. On return he analyses the whisky and finds that it contains only $1.5$ percent of the $13 \mathrm{H}$ radioactive as compared to a recently purchased bottle marked ' 8 years old'. Estimate the time of that unsuccessf...
Read More →When charcoal is prepared from a living tree,
Question: When charcoal is prepared from a living tree, it shows a disintegration rate of $15.3$ disintegration of ${ }^{14} \mathrm{C}$ per gram per minute. A sample from an ancient piece of charcoal shows ${ }^{14} \mathrm{C}$ activity to be $12.3$ disintegration per gram per minute. How old is this sample? Half-life of ${ }^{14} \mathrm{C}$ is $5730 \mathrm{y}$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{1}{\sqrt[3]{x}} d x=?$ A. $\frac{3}{2} \mathrm{x}^{2 / 3}+C$ B. $\frac{3}{2 x^{2 / 3}}+C$ C. $\frac{2}{3 x^{2 / 3}}+C$ D. $\frac{2}{3} \mathrm{x}^{3 / 2}+\mathrm{C}$ Solution:...
Read More →238U decays to 206Pb with a half-life of 4.47×109y.
Question: ${ }^{238} \mathrm{U}$ decays to ${ }^{206} \mathrm{~Pb}$ with a half-life of $4.47 \times 10^{9} \mathrm{y}$. This happens in a number of steps. Can you justify a single half-life for this chain of processes? A sample of rock is found to contain $2.00 \mathrm{mg}$ of ${ }^{238} \mathrm{U}$ and $0.600 \mathrm{mg}$ of ${ }^{206} \mathrm{~Pb}$. Assuming that all the lead has come from uranium, find the life of the rock. Solution:...
Read More →A point source emitting alpha particles is placed at a distance of
Question: A point source emitting alpha particles is placed at a distance of $1 \mathrm{~m}$ from a counter which records any alpha particle falling on its $1 \mathrm{~cm}^{2}$ window. If the source contains $6.0 \times 10^{16}$ active nuclei and the counter records a rate of 50000 counts/second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt[3]{x} d x=?$ A. $\frac{3}{4} \mathrm{x}^{3 / 4}+\mathrm{C}$ B. $\frac{4}{3} \mathrm{x}^{3 / 4}+\mathrm{C}$ C. $\frac{3}{4} x^{4 / 3}+C$ D. $\frac{4}{3} \mathrm{x}^{4 / 3}+\mathrm{C}$ Solution:...
Read More →4×1023 tritium atoms are contained in a vessel.
Question: $4 \times 10^{23}$ tritium atoms are contained in a vessel. The half-life of decay of tritium nuclei is $12.3 y$. Find (a) the activity of the sample, (b) The number of decays in the next 10 hours (c) the number of decays in the next $6.15 \mathrm{y}$. Solution:...
Read More →Carbon (Z=6) with mass number 11 decays to boron (Z=5).
Question: Carbon $(Z=6)$ with mass number 11 decays to boron $(Z=5)$. (a) Is it a $\beta^{+}$-decay or a $\beta^{-}$decay? (b) The half-life of the decay scheme is $20.3$ minutes. How much time will elapse before a mixture of $90 \%$ carbon-11 and $10 \%$ boron-11 (by the number of atoms) converts itself into a mixture of $10 \%$ carbon- 11 and $90 \%$ boron- 11 ? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{1}{x^{3}} d x=?$ A. $\frac{-3}{\mathrm{x}^{2}}+\mathrm{C}$ B. $\frac{-1}{2 \mathrm{x}^{2}}+\mathrm{C}$ C. $\frac{-1}{3 \mathrm{x}^{2}}+\mathrm{C}$ D. $\frac{\mathrm{x}^{-2}}{2}+\mathrm{C}$ Solution:...
Read More →57Co decays to 57Fe by ????+-emission. The resulting 57Fe is in its excited
Question: ${ }^{57}$ Co decays to ${ }^{57} \mathrm{Fe}$ by $\beta^{+}$-emission. The resulting ${ }^{57} \mathrm{Fe}$ is in its excited state and comes to the ground state by emitting $\gamma$ rays. The half-life of $\beta^{+}$-decays is 270 days and that of the $\gamma$ emission is $10^{-8} \mathrm{~s}$. A sample of ${ }^{57}$ Co gives $5.0 \times 10^{9} \mathrm{gamma}$ rays per second. How much time will elapse before the emission rate of gamma rays drops to $2.5 \times 10^{9}$ per second? So...
Read More →The selling rate of a radioactive isotope is decided by its activity.
Question: The selling rate of a radioactive isotope is decided by its activity. What will be the second -hand rate of a one month old ${ }^{32} \mathrm{P}$ ( $\mathrm{t}_{1 / 2}=14.3$ days) source if it was originally purchased for 800 rupees? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x^{5 / 3} d x=?$ A. $\frac{3}{5} \mathrm{x}^{2 / 3}+\mathrm{C}$ B. $\frac{8}{3} \mathrm{x}^{8 / 3}+C$ C. $\frac{3}{8} \mathrm{x}^{8 / 3}+C$ D. $\frac{5}{3} \mathrm{x}^{8 / 3}+C$ Solution:...
Read More →The half-life of a radioisotope is 10 h.
Question: The half-life of a radioisotope is $10 \mathrm{~h}$. Find the total number of disintegrations in the tenth hour measured from a time when the activity was $1 \mathrm{Ci}$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x^{6} d x=?$ A. $7 x^{7}+C$ B. $\frac{x^{7}}{7}+C$ C. $6 \mathrm{x}^{5}+\mathrm{C}$ D. $6 \mathrm{x}^{7}+\mathrm{C}$ Solution:...
Read More →The half-life of 226Ra is 1602 y.
Question: The half-life of ${ }^{226} \mathrm{Ra}$ is $1602 \mathrm{y}$. Calculate the activity of $0.1 \mathrm{~g}$ of $\mathrm{RaCl}_{2}$ in which all the radium is in the form of ${ }^{220} \mathrm{Ra}$. Taken atomic weight of Ra to be $226 \mathrm{~g} / \mathrm{mol}$ and that of $C l$ to be $35.5 \mathrm{~g} / \mathrm{mol}$. Solution:...
Read More →The count rate from a radioactive sample falls from
Question: The count rate from a radioactive sample falls from $4.0 \times 10^{6}$ per second to $1.0 \times 10^{6}$ per second in 20 hours. What will be the count rate 100 hours after the beginning? Solution:...
Read More →Solve this following
Question: Evaluate: $\int\left\{\frac{2-3 \sin x}{\cos ^{2} x}\right\} d x$ Ans. $2 \tan x-3 \sec x+C$ Solution:...
Read More →A certain sample of a radioactive material decays at
Question: A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample? (b) What is its half-life? Solution:...
Read More →Solve this following
Question: Evaluate: $\int \frac{\sec ^{2} x}{\operatorname{cosec}^{2} x} d x$ Ans. $\tan x-x+C$ Solution:...
Read More →The decay constant of
Question: The decay constant of ${ }^{235} \mathrm{U}$ is $4.9 \times 10^{-18} \mathrm{~s}^{-1}$. (a) What is the average- life of ${ }^{235} \mathrm{U}$ ? (b) What is the half-life of ${ }^{235} \mathrm{U}$ ? (c) By what factor does the activity of $a^{235} \mathrm{U}$ sample decrease in $9 \times 10^{8}$ years? Solution:...
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