Law of Radioactivity

Q. The half-life of a radioactive substance is $30$ minutes. The time (in minutes) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is

1. $60$
2. $15$
3. $30$
4. $45$

Q. Radioactive material $A$ has decay constant $8\lambda$ and material $B$ has decay constant $\lambda$. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material B to that A will be $\frac{1}{e}$?

1. $\frac{1}{9\lambda }$
2. $\frac{1}{\lambda }$
3. $\frac{1}{7\lambda }$
4. $\frac{1}{8\lambda }$

Q. the half life of a radioactive nucleus is 50 days. the time interval (t2-t1) between the time t2 when 2/3 of it has decayed and the time t1 when 1/3 of it had decayed as

Q.

X and Y are two radioactive substances having ${\mathrm{N}}_1\mathrm{and}{\mathrm{N}}_2$nuclei. The half-life of X is the half-life of Y.After three half lives of Y , The ratio of ${\mathrm{N}}_1\mathrm{and}{\mathrm{N}}_2$will be equal to?

1. $\frac{8}{1}$

2. $\frac{1}{8}$

3. $\frac{3}{1}$

4. $\frac{1}{3}$

Q. 5.) The half life of radioactive radon is 3.8 days. The time at the end of which (1/20)th of radon sample will remain undecayed (given log10e= .4343) is

Q. The binding energy per nucleon for $C^{12}$ is $7.68MeV$ and that for $C^{13}$ is $7.5MeV$. The energy required to remove a neutron from $C^{13}$ is

1. $5.34MeV$
2. $5.5MeV$
3. $9.5MeV$
4. $9.34MeV$

Q. In a radioactive sample ${}_{19}^{40}K$ nuclei either decay into stable ${}_{20}^{40}Ca$ nuclei with decay constant $4.5\times {10}^{-10}$ per year or into stable ${}_{18}^{40}Ar$ nuclei with decay constant $0.5\times {10}^{-10}$ per year. Given that in this sample all the stable ${}_{20}^{40}Ca$ and ${}_{18}^{40}Ar$ nuclei are produced by the ${}_{19}^{40}K$ nuclei only. In time $t\times {10}^9$ years, if the ratio of the sum of stable ${}_{20}^{40}Ca$ and ${}_{18}^{40}Ar$ nuclei to the radioactive ${}_{19}^{40}K$ nuclei is $99$, the value of t will be? [Given: In $10=2.303$]

1. 1.15
2. 9.2
3. 2.3
4. 4.6

Q.

Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$ they have the same number of nuclei. Find the time interval at which the ratio of the number of nuclei of A to those of B will be $\frac{1}{e^2}$.

Q. $200\text{MeV}$ of energy may be obtained per atom, in the nuclear fission reaction of $U^{235}$. A nuclear reactor is generating a constant power of $1000\text{kW}$. The number of atoms undergoing fission per second is,

1. $3.125\times {10}^{16}$
2. $6.25\times {10}^{16}$
3. $1.25\times {10}^{16}$
4. $2.5\times {10}^{16}$

Q. Half-life of $B{i}^{210}$ is $5$ days. If we start with $50,000$ atoms of this isotope, the number of atoms left after $10$ days is

1. $5,000$
2. $25,000$
3. $12,500$
4. $20,000$

Q. Ten percent of a radioactive sample has decayed in $1\text{day}$. After $2\text{days}$, the decayed percentage of nuclei will be

1. $81\%$
2. $19\%$
3. $20\%$
4. $50\%$

Q. A freshly prepared radioactive source of half life $2\text{hours}30\text{minutes}$ emits radiation which is $64\text{times}$ the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

Q. Two radioactive materials $A$ and $B$ have decay constants $10\lambda \text{and}\lambda ,$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $\frac{1}{e}$ after a time:

1. $\frac{1}{9\lambda }$
2. $\frac{1}{10\lambda }$
3. $\frac{1}{11\lambda }$
4. $\frac{11}{10\lambda }$

Q. The activity of a radioactive material is $6.4\times {10}^{–4}$ curie. Its half life is $5\text{days}$. The activity will become $5\times {10}^{–6}$ curie after

1. $25\text{days}$
2. $35\text{days}$
3. $15\text{days}$
4. $7\text{days}$

Q. In 4g atom of Ag, calculate 1. Amount of Ag 2. Weight of one atom of Ag.

Q. The half-life of 215 At is 100 $\mu s$. The time taken for the radioactivity of a sample of 215 At to decay to $\frac{1}{{16}^{th}}$ of its initial value is

1. $300\mu s$
2. $400\mu s$
   
3. $6.3\mu s$
   
4. $40\mu s$
   

Q. A radioactive nucleus $A$ with a half-life $T$, decays into a nucleus $B$. At $t=0$, there is no nucleus $B$. At some time $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by:

1. $t=\frac{T}{\log \left(1.3\right)}$
2. $t=T\frac{\log 1.3}{\log 2}$
3. $t=\frac{T}{\log \left(1.3\right)}$
4. $t=T\log \left(1.3\right)$

Q.

Radioactivity ${}^{131}\text{I}$ has a half-life of 8.0 days. A sample containing ${}^{131}\text{I}$ has activity $20\mu \text{Ci}$ (a) What is its activity at t = 4.0 days ? (b) What is its decay constant at t = 4.0 days ?

Q. The radioactive sources $A$ and $B$ of half lives of $2\text{hr}$ and $4\text{hr}$ respectively, initially contain the same number of radioactive atoms. At the end of 2 hours, their rates of disintegration are in the ratio :

1. $4:1$
2. $2:1$
3. $\sqrt{2}:1$
4. $1:1$

Q.

The activity of a radioactive substance falls from 700 s^-1 to 500 s^-1 in 30 minutes. Its half-life is close to

1. $66min$

2. $62min$

3. $52min$

4. $72min$

Q. What is the mass of one Curie of$U^{234}$

1. $3.7\times {10}^{10}gm$
   
2. $1.44\times {10}^{-11}gm$
   
3. $2.348\times {10}^{23}gm$
   
4. $6.25\times {10}^{-34}gm$

Q.

What is ${}^{n}C_r$ in probability?

Q. The radioactivity of a sample is X at time $t_1$ and Y and a time $t_2$. If the mean life time of the specimen is $\tau$, the number of atoms that have disintigrated in the time interval $t_1-t_2$ is

1. $X{t}_1-Y{t}_2$
2. $X-Y$
3. $\frac{X-Y}{\tau }$
4. $(X-Y)\tau$

Q.

Natural water contains a small amont of tritium ${(}_1^{3}H)$. This isotope beta-decays 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 per cent of the ${(}_1^{3}H)$. radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.

Q. Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
(where $\lambda$ is the decay constant)

1. $\frac{ln\left(2\right)}{\lambda }$
2. $\frac{ln\left(\frac{3}{2}\right)}{\lambda }$
3. $\frac{2ln\left(2\right)}{\lambda }$
4. $\frac{1}{2}\frac{ln\left(2\right)}{\lambda }$

Q.

The wavelength of the radiation emitted by a body depends upon

1. the nature of its surface

2. the temperature of its surface

3. all the above factors

4. the area of its surface

Q. What is the mass of KClO3 that will liberate 11.35litre O2 at STP?

Q.

90% of the active nuclei present in a radioactive sample are found to remain undecayed after 1 day. The percentage of undecayed nuclei left after two days will be

1. 85 %
2. 81 %
3. 80 %
4. 79 %

Q. In an ore containing uranium, the ratio of $\text{U}-238$ to $\text{Pb}-206$ is $3.$ Assuming that all the lead present in the ore is the final stable product of $\text{U}-238.$ If age of the ore is $1.868\times {10}^n$ years. The value of the $n$ is (integer only).
(Take the half life of $\text{U}-238$ to be $4.5\times {10}^9$ years. $(\ln \frac{4}{3}=0.2876)$

Q. half-life of 1 month has thea331. A radioactive sample withlabel: Activity=2 microcurie on 1-3-2013. What was its(AIPMT)activity before 2 months?(b) 4 microcuriefa) 8 microcurie(d) 0.5 microcurie(c) 1 microcurie