Half and Average Life

Q.

The half-life period of radon is 3.8 days. After how many days will only one-twentieth of the radon sample be left over?

1. 12.65 days
2. 24.75 days
3. 42.35 days
4. 16.54 days

Q.

A radioactive material decays by simulataneous emission of two particles with half - lives 1620 and 810 years. The time after which one - fourth of the material remains, is

1. 1080 years

2. 3240 years

3. 2430 years

4. 4860 years

Q.

The fraction of a radioactive material that remains active after time $t$ is $\frac{9}{16}$. The fraction which remains active after time $\frac{t}{2}$ will be

1. $\frac{4}{5}$

2. $\frac{7}{8}$

3. $\frac{3}{5}$

4. $\frac{3}{4}$

Q.

The half-life for radioactive decay of ${}^{14}C$ is 5730 yr. An archaeological artifact containing wood had only $80\%$ of the ${}^{14}C$ found in a living tree. Estimate the age of the sample.

Q.

A sample of uranium rock from moon contains equimolar amounts of $U^{238}$ and $P{b}^{206}$. The age of the rock will be $(t_{\frac{1}{2}}for{U}^{238}=4.5\times {10}^{9}yrs)$

1. $4.5\times {10}^{9}yrs.$

2. $9.0\times {10}^{9}yrs.$

3. $13.5\times {10}^{9}yrs.$

4. $2.25\times {10}^{9}yrs.$

Q. A $0.50\text{g}$ sample of rock was found to have $2.5\times {10}^{-6}\text{mol}$ of ${}_{19}^{40}K(t_{1/2}=1.3\times {10}^9\text{years})$ and $7.5\times {10}^{-6}{\text{mol of}}_{20}^{40}Ca$. How old is the rock?

1. $1.3\times {10}^9\text{years}$
2. $2.6\times {10}^9\text{years}$
3. $6.5\times {10}^8\text{years}$
4. $5.2\times {10}^9\text{years}$

Q.

On analysis a sample of uranium ore was found to contain 0.277 g of ${}_{82}P{b}^{206}$ and 1.667 g of ${}_{92}S{i}^{238}.$ The half-life period of $U^{238}is4.51\times {10}^9$ years. If all the lead were assumed to have come from the decay of ${}_{92}S{i}^{238},$ what is the age of earth?

1. $1.09\times {10}^{10}years.$
2. 
   $5.20\times {10}^{3}years.$
3. 
   $1.14\times {10}^{9}years.$
4. $1.75\times {10}^{6}years.$

Q. In a sample of wood, the reading of a counter is $32\text{dpm}$ and in fresh sample of tree it is $122\text{dpm}$. Due to an error, the counter gives the reading 2 dpm in absence of ${}^{14}C$. The half-life of ${}^{14}C$ is 5770 years. The approximate age (in years) of wood sample is:

1. $57,570$
2. $11,540$
3. $7997.2$
4. $15140$

Q. A radioactive nuclide is produced at a constant rate of $\alpha$ per second. It's decay constant is $\lambda$. If $N_0$ be the no. of nuclei at time $t=0$, then max. no. of nuclei possible are:

1. $N_0$
2. $N_0+\frac{\alpha }{\lambda }$
3. $\alpha /\lambda$
4. $\frac{\lambda }{\sigma }+N_{0}s$

Q.

The radioactive decay, ${}_{83}B{i}^{211}\to {}_{81}T{l}^{207},$ takes place in 10 L closed container at $0^{\circ }C.$ Half - life of ${}_{83}B{i}^{211}$ is 2.15 min. Starting with 1 mole of ${}_{83}B{i}^{211}$, the pressure developed in the container after 4.30 min. will be

1. 2.24 atm

2. 22.4 atm

3. 16.8 atm

4. 1.68 atm

Q. The half-life period of radon is 3.8 days. After how many days will only one-twentieth of radon sample be left over?

1. 12.65 days
2. 24.75 days
3. 42.35 days
4. 6.5 days

Q. Half life of radioactive decay of $C^{14}$ is $5730$ years. How much time it will take so that $25\%$ of $C^{14}$ was found in sample ?

1. $5730years$
2. $11460years$
3. $22920years$
4. $930years$

Q. The disintegration rate of a certain radioactive sample at any instant is 4750 dpm (disintegration per minute). Five minutes later, the rate becomes 2700 dpm. Calculate half-life of sample.

1. 6.1328 min
2. 9.3328 min
3. 7.2328 min
4. None of these

Q. Ten grams of ${}^{60}Co$ kept in an open container $\beta$ decays with a half-life of 270 days. The decay products are constantly flushed out. The weight of the material inside the container after 540 days will be very nearly:

1. 5 g
2. 10 g
3. 2.5 g
4. 1.25 g

Q. Which of the following metal can be reduced by carbon reduction as well as self reduction?

1. Fe
2. Al
3. Pb
4. None of these

Q. The volume occupied by 0.01 moles of helium gas at STP is:

1. $0.224l$
2. $2240l$
3. $22.4l$
4. $2.24l$

Q. When ${}_{92}{U}^{238}$ decays it emits an $\alpha$ - particle. The new nuclide in turn emits a $\beta$ - particle to give another nuclide X. The mass number and atomic number of X are respectively :

1. 234 and 91
2. 234 and 96
3. 232 and 88
4. 234 and 88

Q. ${}_{92}{U}^{235}$ nucleus absorbs a neutron and disintegrate in ${}_{54}{Xe}^{139}$, ${}_{38}{Sr}^{94}$ and $X$ so, what will be product $X$?

1. $\alpha$-particle
2. $\beta$-particle
3. $3$-neutrons
4. $2$-neutrons

Q. A $0.50\text{g}$ sample of rock was found to have $2.5\times {10}^{-6}\text{mol}$ of ${}_{19}^{40}K(t_{1/2}=1.3\times {10}^9\text{years})$ and $7.5\times {10}^{-6}{\text{mol of}}_{20}^{40}Ca$. How old is the rock?

1. $6.5\times {10}^8\text{years}$
2. $1.3\times {10}^9\text{years}$
3. $2.6\times {10}^9\text{years}$
4. $5.2\times {10}^9\text{years}$

Q. The decay constant of ${}^{238}Uis1.54\times {10}^{-10}y{r}^{-1}$. What will be the average life of a sample of ${10}^{20}such{}^{238}U$ nuclei?

1. 3.25 billion years
2. 6.49 million years
3. 3.25 million years
4. 6.49 billion years

Q. Red phosphorus is heated with sulphur in an atmosphere of carbon dioxide to produce:

1. $P{S}_3$
2. $P_4{S}_3$
3. $P_2{S}_3$
4. $P{S}_4$

Q. Consider following radioactive decay of
$I{:}_{92}U\stackrel{-a}{\to }{}_{90}Th$
$II{:}_{90}U\stackrel{-a}{\to }{}_{88}Ra$
In which case group of the parent and daughter element remain uncharged ?

1. in I
2. in II
3. in both (a) and (b)
4. in none of these

Q. ${}_{921}{U}^{238}$ by successive radioactivity decays changes to ${}_{82}P{b}^{206}$.A sample of uranium ore was analyzed and found to contain 1.0g of $U^{238}$and $0.1$g of $P{b}^{206}$. Assuming that all the $P{b}^{206}$had accumulated due to decay of $U^{238}$, find out the age of the ore ?(Half life of $U^{238}=4.5\ast {10}^{9}years).$

1. $t=7.1\ast {10}^5$ years
2. $t=7.1\ast {10}^8$ years
3. $t=7.1\ast {10}^6$ years
4. $t=7.1\ast {10}^3$ years

Q. ${}^{6}4\text{Cu}$ (half-life = $12.8$hr) decays by ${\beta }^{-}$ emission ($38\%$), ${\beta }^{+}$ emission ($19\%$) and electron capture ($43\%$). Write the decay product and calculate partial half-lives for each of the decay processes.

Q. ${}_{92}{\text{U}}^{238}$ by successive radioactive decays changes to ${}_{82}{\text{Pb}}^{206}$. A sample of uranium ore was analyzed and found to contain 1.0 g of $U^{238}$ and 0.1 g of $P{b}^{206}$. Assuming that all the $P{b}^{206}$ had accumulated due to decay of $U^{238}$, find out the age of the ore. (Half life of $U^{238}=4.5\times {10}^{9}years$)

1. $t=3.5\times {10}^{8}years$
2. $t=7.1\times {10}^{8}years$
3. $t=14.2\times {10}^{8}years$
4. $t=7.1\times {10}^{7}years$

Q. Match List 1 with List 2:

Q. The half-life of ${}^{198}Au$ is 2.7 days. Calculate the decay constant. Take atomic weight of ${}^{198}Au$ to be 198 g $mo{l}^{-1}$.

1. $2.9\times {10}^{-10}{s}^{-1}$
2. $2.9\times {10}^{-8}{s}^{-1}$
3. $2.9\times {10}^{-6}{s}^{-1}$
4. $2.9\times {10}^{-4}{s}^{-1}$

Q. ${}_Z^A{X}^{\ast }{\to }_Z^{A}X+k$

1. $\alpha particle$
2. $\beta particle$
3. $\gamma particle$
4. None of the above

Q. The radioactive decay ${}_{83}{Bi}^{211}{⟶}_{81}{Ti}^{207}$, takes place in $100L$ closed vessel at ${27}^{o}C$. Starting with $2$ moles of ${}_{83}{Bi}^{211}(t_{1/2}=130sec)$, the pressure development in the vessel after $520$sec will be:

1. $0.2155$ atm
2. $1.875$ atm
3. $0.4618$ atm
4. $4.618$ atm

Q. ${}_{92}^{238}U$ by successive radioactive decays changes to ${}_{82}^{260}Pb$. A sample of uranium ore was analysed and found to contain 1.0g ${}^{238}U$ and 0.1 g ${}^{206}Pb$. Assuming that $6^{260}Pb$ has accumulated due to decay of ${}^{238}U$, find out the age of the ore? ($T_{50}$ of ${}^{238}U$ is $4.5\times {10}^9$ years).

1. $2\times {10}^9$ years
2. $7.1\times {10}^8$ years
3. $4\times {10}^9$ years
4. $6.2\times {10}^9$ years