IISER Physics - Nuclear Physics and Radioactivity
Exam Duration: 45 Mins Total Questions : 30
The ratio of the nuclear radii of Cs135 to Ca40 is
- (a)
1.35
- (b)
3.375
- (c)
1.84
- (d)
1.5
Find the density of \(^{12}_6C\) nucleus.
- (a)
2.7X10-17 kg/m3
- (b)
2.4X1017 kg/m3
- (c)
2.7X1015 kg/m3
- (d)
2.4X10-15 kg/m3
Assuming that all laws of thermodynamics can be applied to a nucleus, the \(\alpha\)-decay of a nucleus may be regarded as an
- (a)
isothermal process
- (b)
isobaric process
- (c)
adiabatic process
- (d)
isochoric process
Which one of the following processes represents a \(\gamma \ decay\)?
- (a)
\(^A_ZX+\gamma\rightarrow ^A_{Z-1}X+a+b\)
- (b)
\(^A_ZX+^1_0n\rightarrow ^{A-3}_{Z-2}X+c\)
- (c)
\(^A_ZX+^o_{-1}e\rightarrow ^A_{Z-1}X+g\)
- (d)
\(^A_ZX^*\rightarrow ^A_{Z}X+f\)
The half-life of 131I is 8 day. Given a sample of 131I at time t=0, we can assert that
- (a)
no nucleus will decay before t=4 days
- (b)
no nucleus will decay beore t=8 days
- (c)
all nuclei will decay before t=16 days
- (d)
given nucleus may decay at any time after t=0
If one starts with one curie of radioactive substance (T1/2=12h), then the activity left after a period of 1 week will be about
- (a)
1 curie
- (b)
120 micro curie
- (c)
60 micro curie
- (d)
8 mili curie
A radioactive isotope X with a half-life of 1.37X109yr decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y which were in the ratio of 1:7. The age of the rock is
- (a)
1.96X108 yr
- (b)
3.85X109yr
- (c)
4.11X109yr
- (d)
9.59X109yr
A and B are two radioactive substances whose half-lives are 1 and 2 yr respectively. Initially, 10g of A and 1g of B is taken. The time (approximate) after which they will have same quantity remaining is
- (a)
6.62 yr
- (b)
5 yr
- (c)
3.2yr
- (d)
7 yr
The ratio of half-life and mean life of a radioactive sample is
- (a)
ln 2
- (b)
1
- (c)
\(1\over ln \ 2\)
- (d)
\(1\over 2\ ln \ 2\)
From a newly formed radioactive substance (Half-life 2 h), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is
- (a)
6h
- (b)
12h
- (c)
24h
- (d)
128h
Let mp be the mass of a proton mn the mass of a neutron, M1 the mass of a \(^{20}_{10}Ne\) nucleus and M2 the mass of a \(^{40}_{20}Ca\)
- (a)
M2=2M1
- (b)
M2>2M1
- (c)
M2<2M1
- (d)
M1<10(mn+mp)
Which of the following is a wrong description of binding energy of a nucleus?
- (a)
It is the energy required to break a nucleus into its constituent nucleons.
- (b)
It is the energy made available when free nucleons combined to form a nucleus
- (c)
It is the sum of the rest mass energies of its nucleons minus the rest mass energy of the nucleus
- (d)
It is the sum of the kinetic energy of all the nucleons in the nucleus.
The binding energy per nucleon of O16 is 7.97MeV and that of O17 is 7.75MeV. The energy required to remove a neutron from O17 in MeV is
- (a)
3.52
- (b)
3.64
- (c)
4.23
- (d)
7.86
For a substance, the average life for \(\alpha-\)emission is 1620yr and for \(\beta-\)emission is 405yr. After how much time, the \(1\over 4\) of the material remains after \(\alpha \ and \ \beta\) emission?
- (a)
1500yr
- (b)
300yr
- (c)
449yr
- (d)
810yr
The half-life of radioactive polonium(Po) is 138.6day. For ten lakh polonium atoms, the number of disintegrations in 24 h is
- (a)
2000
- (b)
3000
- (c)
4000
- (d)
5000
The radioactivity of a sample is R1 at a time T1 and R2 at a time T2. If the half-life of the specimen is T, then the number of nuclei that have disintegrated in the time (T2-T1) is proportional to
- (a)
(R1T1-R2T2)
- (b)
R1+R2
- (c)
(R1XR2)/T
- (d)
(R1-R2)R
Suppose we consider a larger number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1yr. After 1 yr,
- (a)
all the containers will have 5000 atoms of the material
- (b)
all the containers will contain the same number of atoms of the material but that number will only be approximately 5000
- (c)
the containers will in general have different number of the atoms of the material but their average will be close to 5000
- (d)
None of the containers can have more than 5000 atoms.
Tritium is an isotope of hydrogen whose nucleus triton contains 2 neutrons and 1 proton. Free neutrons decay into \(p+\bar e+\bar v\). If one of the neutrons in triton decays, it would transform into He3 nucleus. This does not happen. This is, because
- (a)
triton energy is less than that of a He3 nucleus
- (b)
The electron created in the \(\beta\)-decay process cannot remain in the nucleus
- (c)
both the neutrons in triton have to decay simultaneously resulting in a nucleus with 3 protons, which is not a He3 nucleus
- (d)
free neutrons decay due to ecternal perturbations which is absent in a triton nucleus
Heavy stable nuclei have more neutrons than protons. This is because of the fact that
- (a)
neutrons are heavier than protons
- (b)
electrostatic force between protons and repulsive
- (c)
neutrons decay into protons through beta decay
- (d)
nuclear forces between neutrons are weaker than that between protons
In a nuclear reactor, moderators slow down the neutrons which come out in a fission process. The moderator used light nuclei. Heavy nuclei will not serve the purpose, because
- (a)
They will break up
- (b)
elastic collision of neutrons with heavy nuclei will not slow them down
- (c)
the net weight of the reactor would be unbearably high
- (d)
substances with heavy nuclei do not occur in liquid or gaseous state at room temperature
Match the categories of nuclei given in column I with their examples given in column II and select the correct option from the choices given below.
column I | column II |
---|---|
A. Isotopes | 1. 6C14, 7N14 |
B. Isobars | 2. 3Li7, 4Be8 |
C. Isotones | 3. 1H1,1H2,1H3 |
- (a)
A B C 3 2 1 - (b)
A B C 2 1 3 - (c)
A B C 3 1 2 - (d)
A B C 1 2 3
Assume that a neutron breaks into a proton and an electron. The energy released during this process in (mass of neutron = 1.6725X10-27kg, mass of proton=1.6725X10-27 kg, mass of electron =9X10-31kg)
- (a)
0.73 MeV
- (b)
7.10 MeV
- (c)
6.30 MeV
- (d)
5.4 MeV
After absorbing a slowly moving neutron of mass mn (momentum~0) a nucleus of mass M breaks into two nuclei of masses m1 and 5m1(6m1=M+mn), respectively. If the de-Broglie wavelength of the other nucleus will be
- (a)
25\(\lambda\)
- (b)
5\(\lambda\)
- (c)
\(\lambda\over 5\)
- (d)
\(\lambda\)
The half-life of a radioactive substance is 20min.The approximate time interval (t2 - t1) between the time t2 when \(2\over 3\) of it has decayed and time t1 when \(1\over 3\) of it had decayed is
- (a)
14 min
- (b)
20 min
- (c)
28min
- (d)
7 min
A nucleus of mass M+\(\Delta m\) is at rest and decays into two daughter nuclei of equal mass \(M\over 2\) each. Speed of light is c. The binding energy per nucleon for the parent nucleus is E1 and that for the daughter nuclei is E2. Then
- (a)
E2=2E1
- (b)
E1>E2
- (c)
E2>E1
- (d)
E1=2E2
If the binding energy per nucleon in \(^7_3Li \ and \ ^4_2He\) nuclei are 5.60MeV and 7.06MeV respectively, then in the reaction \(p+^7_3Li\rightarrow 2^4_2He\) energy of proton must be
- (a)
28.24 MeV
- (b)
17.28 MeV
- (c)
1.46MeV
- (d)
39.2 MeV
Starting with a sample of pure 66Cu, 7/8 of it decays into Zn in 15min. The corresponding half-life is
- (a)
10min
- (b)
15min
- (c)
5min
- (d)
\(7{1\over 2}\) min
A nuclear transformation is denoted by X(n,\(\alpha\))\(\rightarrow ^7_3Li\). Which of the following is the nucleus of element X?
- (a)
\(^{12}_6 C\)
- (b)
\(^{10}_5 B\)
- (c)
\(^9_5B\)
- (d)
\(^{11}_4Be\)
A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:1. The ratio of their nuclear sizes will be
- (a)
21/3 : 1
- (b)
1:31/2
- (c)
31/2 : 1
- (d)
1:21/3
The ratio of radii of nuclei 13Al27 and 52XA is 3:5. the number of neutrons in the nuclei of X will be
- (a)
52
- (b)
73
- (c)
125
- (d)
13