“Maturity is often more absurd than youth and very frequently is most unjust to youth”

– Thomas A. Edison

^{th}December 2008. A few multiple choice practice questions on nuclear physics were discussed in the post dated 30

^{th}December 2008, followed by a free response practice question in the post dated 13

^{th}January 2009. You can access all those posts by clicking on the label ‘nuclear physics’ below this post.

Today we will discuss a few more multiple choice practice questions in this section:

**(1)** The density of nuclear matter is

(a) directly proportional to the number protons in the nucleus

(b) directly proportional to the number neutrons in the nucleus

(c) directly proportional to the square of the number of nucleons in the nucleus

(d) directly proportional to the 4^{th} power of the number of nucleons in the nucleus

(e) independent of the number nucleons in the nucleus

The correct option is (e). Nuclear radius *R* is given by

*R =R*_{0}*A*^{1/3}

where *R*_{0} = 1.2×10^{–15} m and *A* is the mass number (or, nucleon number).

The volume of the nucleus which is proportional to *R*^{3} is therefore proportional to the mass number *A*. Since the density is the ratio of mass to volume, it follows that the density of the nucleus is independent of the mass number and is constant (approximately 2.3×10^{17} kgm^{–3}).

**(2) **Nuclear force is

(a) short range and charge dependent

(b) long range and charge dependent

(c) short range and charge independent

(d) long range and charge independent

(e) electromagnetic in nature

Nuclear force is a *short range* force produced by the exchange of π-mesons between the nucleons.

The force between a proton and a neutron is produced because of the exchange of *charged* π-mesons (π^{+} and π^{–}) where as the force between two protons and that between two neutrons is produced by the exchange of *uncharged* π-mesons (π^{0}).

Nuclear force is a strong attractive force (in fact, the strongest natural force) and is *charge independent*.

The correct option is (c).

**(3)** In the nuclear reaction given by

_{7}N^{14} + _{2}He^{4} = _{m}X^{n} + _{1}H^{1}, what is the nucleus _{m}X^{n}?

(a) Oxygen of mass number 18

(b) Nitrogen of mass number 18

(c) Oxygen of mass number 16

(d) Oxygen of mass number 17

(e) Nitrogen of mass number 17

Since the total mass number on the left hand side of the equation is 18, the mass number of X has to be 17 (for balancing the equation).

[14 + 4 = n + 1 from which n = 17]

The atomic number of X (or, the number of protons in the nucleus X) is 8 since the total atomic number on the left hand side of the equation is 9.

[7 + 2 = m + 1 from which m = 8]

Therefore the nucleus X is that of oxygen (_{8}O^{17})

**(4) **Cobalt 60 is a radioactive source with a half life of 5.27 years. You may take it as 5 years. After how many years will the activity of a sample of cobalt 60 be decreased to 1/16 its original activity?

(a) 10 years

(b) 16 years

(c) 20 years

(d) 32 years

(e) 40 years

The activity (number of disintegrations per second) is directly proportional to the number of undecayed nuclei in the sample. Since the number of undecayed nuclei reduces to half the initial value in every half life period, the activity also reduces to half the initial value in every half life period. Therefore, after 5 years the activity becomes half the initial value; after 10 years the activity becomes 1/4 the initial value; after 15 years it becomes 1/8 the initial value and after 20 years the activity becomes 1/16 the initial value. The correct option is (c).

[The activity *A * after *n *half lives is given by *A = A*_{0}/2^{n} where *A*_{0} is the initial activity. Therefore, 1/16 = 1/2^{n }so that 2^{n }= 16 from which *n =* 4. Four half lives = 20 years].

**(5)** In a typical fission reaction, a U^{235} nucleus absorbs a slow neutron and becomes a compound nucleus U^{236} in a highly excited state. U^{236} then undergoes fission, producing two fission fragments (Xe^{140} and Sr^{94}) and two neutrons. Typically what should be the energy of the slow neutron that initiates the fission reaction in U^{235} nucleus?

(a) 25 Mev

(b) 2.5 KeV

(c) 250 eV

(d) 25 eV

(e) 0.025 eV

Neutrons can be absorbed by the U^{235} nuclei if they are of *thermal* energies. Such thermal neutrons have energies of the order of a small fraction of an electron volt as given in option (e).

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