Nucleus: Common Terms

Q. Two radioactive nuclei $\text{A}$ and $\text{B}$ initially contain equal number of radioactive atoms. Source $\text{A}$ has a half-life of $1$-hour and source $\text{B}$ has a half-life of $2$-hours. At the end of $2$-hours, the ratio of the rate of disintegration of $\text{A}$ to that of $\text{B}$ is-

1. $1:2$
2. $2:1$
3. $1:1$
4. $1:4$

Q. A radioactive material decays by simultaneous emissions of two particles with half life of $1400$ years and $700$ years respectively. What will be the time after which, one third of the material remains ?

Take $\ln 3\approx 1.1$

1. $340$ years
2. $740$ years
3. $1110$ years
4. $700$ years

Q.

The distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy K is $r_0$. The distance of the closest approach when the alpha particle is fired at the same nucleus with kinetic energy 2K will be

1. $4r_0$

2. $2r_0$

3. $\frac{r_0}{2}$

4. $\frac{r_0}{4}$

Q. A radioactive sample, at a certain instant of time, has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes, the rate is $1250$ disintegrations per minute. Then, the decay constant (in per minute) is,

1. $0.4\ln 2$
2. $0.2\ln 2$
3. $0.1\ln 2$
4. $0.8\ln 2$

Q. The activity of a radioactive sample falls from $700{\text{s}}^{-1}$ to $500{\text{s}}^{-1}$ in $30$ minutes. It's half life is close to :
$\left(\text{Take}\text{ln 2 = 0.693 and ln 1.4 = 0.336}\right)$

1. $\text{72 min}$
2. $\text{62 min}$
3. $\text{66 min}$
4. $\text{52 min}$

Q. The closest distance of approach of an $\alpha$ - particle travelling with a velocity $v$ towards a stationary nucleus is $d$. For the closest distance to become $\frac{d}{2}$ towards a stationary nucleus of double the charge, the velocity of projection of the $\alpha$- particle has to be

1. $\sqrt{2}v$
2. $2v$
3. $4v$
4. $\sqrt{6}v$

Q. $1\text{g}$ of a radioactive substance disintegrates at the rate of $3.7\times {10}^{10}$ disintegrations per second. The atomic mass of the substance is $226$. Calculate its mean life.

1. $6.2\times {10}^{10}\text{s}$
2. $7.2\times {10}^{10}\text{s}$
3. $8.2\times {10}^{10}\text{s}$
4. $9.2\times {10}^{10}\text{s}$

Q. Match the nuclear processes given in column I with the appropriate option(s) in column II

Column I	Column II
(A) Nuclear fusion	(P) Absorption of thermal neutrons by ${}_{92}^{235}U$
(B) Fission in a nuclear reactor	(Q) ${}_{27}^{60}Co$ nucleus
(C) $\beta$-decay	(R) Energy production in stars via hydrogen conversion to helium
(D) $\gamma$-ray emission	(S) Heavy water
	(T) Neutrino emission

1. $\left(A\right)\to (R,S);\left(B\right)\to (T,S);$
   $\left(C\right)\to (P,Q,R,T);$(D) \rightarrow (P, Q, T)$
2. $\left(A\right)\to \left(R\right);\left(B\right)\to (P,S);$
   $\left(C\right)\to (P,Q,R,T);$(D) \rightarrow (P, Q, R, T)$
3. $\left(A\right)\to (R,T);\left(B\right)\to (P,S);$
   $\left(C\right)\to (P,R,T);$(D) \rightarrow (P, Q, S, T)$
4. $\left(A\right)\to (Q,T);\left(B\right)\to (P,);$
   $\left(C\right)\to (P,R,T);$(D) \rightarrow (P, Q, S, T)$

Q. During the mean life of a radioactive element, the fraction that disintegrates is-

1. $\frac{1}{e}$
2. $\frac{e}{e-1}$
3. $\frac{e-1}{e}$
4. $\frac{e}{e-1}$

Q.

The name of the isotope is cobalt-60. Find the number of protons, mass number, number of electrons and number of neutrons.

Q. A radioactive nucleus decays by two different processes. The half life for the first process is $10\text{s}$ and that for the second is $100\text{s}$. The effective half life of the nucleus is close to

1. $\text{9 sec}$
2. $\text{6 sec}$
3. $\text{55 sec}$
4. $\text{12 sec}$

Q. A radioactive substance decays to ${\left(\frac{1}{16}\right)}^{th}$ of its initial activity in $80$ days. The half life of the radioactive substance expressed in days is ______.

Q. A radioactive sample can decay by two different processes. The half-life for the first process is $T_1$ and that for the second process is $T_2$. The effective half-life $T$ of the radioactive sample is,

1. $T=\frac{T_1-T_2}{T_1{T}_2}$
   
2. $T=\frac{T_1+T_2}{T_1{T}_2}$
   
3. $T=\frac{T_1{T}_2}{T_1+T_2}$
   
4. $T=T_1+T_2$
   

Q.

Write the symbols of three isotopes of carbon.

Q. What is the work done by the field of a nucleus in complete circular orbit of the electron and what if the orbit is elliptical?

Q. At a given instant, say $t=0$, two radioactive substances $A$ and $B$ have equal activities. The ratio $\frac{R_B}{R_A}$ of their activities after time $t$ itself decays with time $t$ as $e^{-3t}$. If the half-life of $A$ is $\ln 2$, the half-life of $B$ is:

1. $\frac{\ln 2}{2}$
2. $4\ln 2$
3. $2\ln 2$
4. $\frac{\ln 2}{4}$

Q. Activities of three radioactive substances $A,B$ and $C$ are represented by the curves $A,B$ and $C$, in the figure. Then their half-lives $T_{\frac{1}{2}}\left(A\right):T_{\frac{1}{2}}\left(B\right):T_{\frac{1}{2}}\left(C\right)$ are in the ratio

1. $2:1:1$
2. $3:2:1$
3. $2:1:3$
4. $4:3:1$

Q. The sodium nucleus ${}_{11}^{23}$ Na contains

1. 11 electrons
2. 12 protons
3. 23 protons
4. 12 neutrons

Q. In a chemical analysis of a rock, the mass ratio of two radioactive isotopes is found to be $100:1$. The mean lives of the two isotopes are $4\times {10}^9\text{years}$ and $2\times {10}^9\text{years}$, respectively. If it is assumed that at the time of formation, atoms of both the isotopes were in equal proportion, calculate the age of rock. Ratio of the atomic weight of the two isotopes is $1.02:1$.
Given ${\log }_e\left(100/1.02\right)=4.58$

1. $1.83\times {10}^9\text{years}$
2. $1.82\times {10}^8\text{years}$
3. $1.83\times {10}^{10}\text{years}$
4. $1.82\times {10}^{11}\text{years}$

Q. The activity of sample of radioactive materials is $A_1$ at time $t_1$ and $A_2$ at time $t_2(t_2>t_1)$. It's mean life is $T$, then

1. $A_2=A_1{e}^{\left(\frac{t_1-t_2}{T}\right)}$
2. $A_2=A_1{e}^{\left(\frac{t_1/t_2}{T}\right)}$
3. $A_1{t}_1=A_2{t}_2$
4. $\frac{A_1-A_2}{t_2-t_1}=\text{Constant}$

Q. Atomic number of a nucleus is Z and atomic mass is M. The number of neutron is

1. M-Z
2. M+Z
3. M
4. Z

Q.

List the reason for the nucleus to exhibit a positive charge.

Q.

The chemical behaviour of an atom depends upon

1. the number of electrons orbiting around its nucleus

2. the number of protons in its nucleus

3. the number of neutrons in its nucleus

4. the number of nucleons in its nucleus.

Q. To determine the half life of a radioactive element, student plots a graph of $\ln \left|\frac{dN\left(t\right)}{dt}\right|$ versus $t$. Here $dN\left(t\right)/dt$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16\text{years}$, the value of $p$ is ____. (Round off the nearest integer) $(e^{4.16}=64.07)$

Q. If mass of neutron is assumed to half of its original value, whereas that of proton is assumed to be twice of its original value, then the atomic mass of ${}_6^{14}C$ will be:

1. same
2. $14.25\%$ less
3. $14.28\%$ more
4. $28.56\%$ less

Q.

Isotopes are atoms having

1. Same number of protons but different number of neutrons

2. Same number of neutrons but different number of protons

3. Same number of protons and neutrons

4. None of the above

Q. If 2 neutrons exert only attractive force, why dont we have a nucleus containing neut

Q.

Consider the following statements

1. All isotopes of an element have the same number of neutrons.
2. Only one isotope of an element can be stable and non-radioactive.
3. All elements can have isotopes.
4. All isotopes of Carbon can form chemical compounds with Oxygen-16.

The correct option regarding an isotope is

1. (iii) and (iv) only

2. (ii), (iii) and (iii) only

3. (i), (ii) and (iii) only

4. (i), (iii) and (iv) only

Q. The three stable isotopes of neon: 20 21 2210 10 Ne, Ne and Ne 10 haverespective abundances of 90.51%, 0.27% and 9.22%. The atomicmasses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.

Q. (a) Two stable isotopes of lithium 63 Li and 73 Li have respectiveabundances of 7.5% and 92.5%. These isotopes have masses6.01512 u and 7.01600 u, respectively. Find the atomic massof lithium. (b) Boron has two stable isotopes, 105B and 115B. Their respectivemasses are 10.01294 u and 11.00931 u, and the atomic mass ofboron is 10.811 u. Find the abundances of 105B and 115 B.