Nuclei

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, the number of P species is 4N0 and that of Q is N0. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

1. 2N0
2. 3N0
3. 9N02
4. 5N02

The power obtained in a reactor using 235U disintegration is 1000 kW. The mass decay of 235U per hour is

1. 10 microgram
2. 20 microgram
3. 40 microgram
4. 1 microgram

Fusion reaction takes place at high temperature because

1. nuclei break up at high temperature
2. atoms get ionised at high temperature
3. kinetic energy is high enough to overcome the Coulomb repulsion between nuclei
4. molecules break up at high temperature

The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be

1. 150 years
2. 200 years
3. 250 years
4. 100 years

A nucleus mnX emits one particle and two particles. The resulting nucleus is

1. m-6n-4Z
2. m-6nZ
3. m-4nX
4. m-4n-2Y

The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

1. 23.6 MeV
2. 2.2 MeV
3. 28.0 MeV
4. 30.2 MeV

The decay constant of a radioisotope is . If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1 - t2)

1. A1t1 - A2t2
2. A1 - A2
3. (A1 - A2)/
4. (A1 - A2)

The mass of a 73Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of 73Li nucleus is nearly

1. 46 MeV
2. 5.6 MeV
3. 3.9 MeV
4. 23 MeV

The activity of a radioactive sample is measured as N0 counts per minute at t = 0 and N0/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

1. e 25
2. 5 e 2
3. 5 10 2
4. 5 e 2

In the nuclear decay given below AZX AZ+1Y A-4Z-1 B* A-4Z-1B, the particles emitted in the sequence are

1. , ,
2. , ,
3. , ,
4. , ,

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

1. isomer of parent
2. isotone of parent
3. isotope of parent
4. isobar of parent

If M(A, Z), Mp and Mn denote the masses of the nucleus AZX, proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its binding energy in MeV, then

1. M(A, Z) = ZMp + (A - Z)Mn - BE
2. M(A, Z) = ZMp + (A - Z)Mn + BE/c2
3. M(A, Z) = ZMp + (A - Z)Mn - BE/c2
4. M(A, Z) = ZMp + (A - Z)Mn + BE

Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be

1. (3)1/3 : 1
2. 1 : 1
3. 1 : 3
4. 3 : 1

Two radioactive materials X1 and X2 have decay constants 5 and respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1e after a time

1. 14
2. e
4. 12

A nucleus AZX has mass represented by M(A, Z). If Mp and Mn denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then

1. B.E. = [ZMp + (A - Z)Mn - M(A, Z)]c2
2. B.E. = [ZMp + AMp - M(A, Z)]c2
3. B.E. = M(A, Z) - ZMp - (A - Z)Mn
4. B.E. = [M(A, Z) - ZMp - (A - Z)Mn]c2

Two radioactive substances A and B have decay constants 5 and respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ( 1e )2 after a time interval

1. 4
2. 2
3. 12
4. 14

In a radioactive decay process, the negatively charged emitted -particles are

1. the electrons produced as a result of the decay of neutrons inside the nucleus
2. the electrons produced as a result of collisions between atoms
3. the electrons orbiting around the nucleus
4. the electrons present inside the nucleus

If the nucleus 2713Al has a nuclear radius of about 3.6 fm, then 12552Te would have its radius approximately as

1. 9.6 fm
2. 12.0 fm
3. 4.8 fm
4. 6.0 fm

The binding energy of deuteron is 2.2 MeV and that of 42He is 28 MeV. If two deuterons are fused to form one 42He then the energy released is

1. 30.2 MeV
2. 25.8 MeV
3. 23.6 MeV
4. 19.2 MeV

In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is , then

1. R1 = R2
2. R1 = R2 e- (t1 - t2)
3. R1 = R2 e (t1 - t2)
4. R1 = R2(t2/t1).

The radius of germanium (Ge) nuclide is measured to be twice the radius of 94Be. The number of nucleons in Ge are

1. 72
2. 73
3. 74
4. 75

In the reaction 21H + 31H 42He + 10n, if the binding energies of 21H, 31H and 42He are respectively a, b and c (in MeV), then the energy (in MeV) released in this reaction is

1. a + b + c
2. a + b - c
3. c - a - b
4. c + a - b

In any fission process the ratio mass of fission productsmass of parent nucleus is

1. equal to 1
2. greater than 1
3. less than 1
4. depends on the mass of the parent nucleus.

Fission of nuclei is possible because the binding energy per nucleon in them

1. increases with mass number at low mass numbers
2. decreases with mass number at low mass numbers
3. increases with mass number at high mass numbers
4. decreases with mass number at high mass numbers.

Which one of the following pairs of nuclei are isotones ?

1. 34Se74, 31Ga71
2. 38Sr84, 38Sr86
3. 42Mo92, 40Zr92
4. 20Ca40, 16S32

If M(A, Z), Mp and Mn denote the masses of the nucleus AZX, proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its binding energy in MeV, then

1. M(A, Z) = ZMp + (A - Z)Mn - BE
2. M(A, Z) = ZMp + (A - Z)Mn + BE/c2
3. M(A, Z) = ZMp + (A - Z)Mn - BE/c2
4. M(A, Z) = ZMp + (A - Z)Mn + BE

If in a nuclear fusion process the masses of the fusing nuclei be m1 and m2 and the mass of the resultant nucleus be m3, then

1. m3 = m1 + m2
2. m3 = |m1 - m2|
3. m3 < (m1 + m2)
4. m3 > (m1 + m2)

A nucleus represented by the symbol AZX has

1. Z neutrons and A - Z protons
2. Z protons and A - Z neutrons
3. Z protons and A neutrons
4. A protons and Z - A neutrons

The half life of radium is about 1600 years. Of 100 g of radium existing now, 25 g will remain unchanged after

1. 4800 years
2. 6400 years
3. 2400 years
4. 3200 years

Solar energy is mainly caused due to

1. burning of hydrogen in the oxygen
2. fission of uranium present in the Sun
3. fusion of protons during synthesis of heavier elements
4. gravitational contraction