# Physics Questions and Answers – Size of the Nucleus

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This set of Physics Online Quiz for IIT JEE Exam focuses on “Size of the Nucleus”.

1. Identify the expression for the nuclear radius from the following.
a) R = R0 ∛A
b) R = R0 √A
c) R = R0 A3
d) R = R0 A2

Explanation: Most of the nuclei of atoms are spherical in structure. The expression for the nuclear radius is given by:
R = R0 ∛A
Where R0 is a constant and A is the mass number. The nuclear radius is measured in Fermi meter.
1 fm = 10-15 m.

2. Who measured the size of the nucleus first?
a) Bohr
b) Einstein
c) Rutherford
d) Geiger and Marsden

Explanation: Rutherford was the form to measure the size of the nuclei of an atom by 1911. He discovered that these were about 104 times smaller than the atoms that constituted them and this was due to the fascinating way that the alpha particles scattered from metal foils.

3. Which of the following is a stable nucleus?
a) The nucleus with even protons and odd electrons
b) The nucleus with even number of protons and neutrons
c) The nucleus with even neutrons and odd protons
d) The nucleus with odd protons and neutrons

Explanation: The nuclei of atoms having even numbers of both protons and neutrons are the most stable ones and this also means that they are less radioactive than nuclides containing even numbers of protons and odd numbers of neutrons.
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4. If the internal energy of a nucleus is high, then it is radioactive.
a) True
b) False

Explanation: Yes, this is a true statement. An atom is said to be unstable, or in other words, radioactive when the forces that it is subjected to it are unbalanced. Therefore, when there is an excess of internal energy, instability of an atom’s nucleus occurs and hence they can become radioactive. This may also result from an excess of either neutrons or protons in the nucleus.

5. A nucleus at rest splits into two nuclear parts having radii in the ratio of 1:3. Find the ratio of their velocities.
a) 1:9
b) 3:1
c) 1:27
d) 27:1

Explanation: Given: R1 = R0 (A1)1/3 and R2 = R0 (A2)1/3
$$\frac {R1}{R2} = (\frac {A1}{A2} ) ^{\frac {1}{3}}$$ or $$\frac {A1}{A2} = (\frac {R1}{R2} )^3 = (\frac {1}{3} )^3$$
$$\frac {A1}{A2} = \frac { 1}{27}$$
So, the ratio of their masses is given as:
$$\frac {m1}{m2} = \frac { 1}{27}$$
According to the principle of conservation of momentum, the magnitude of p1 = magnitude of p2
m1v1 = m2v2
$$\frac {v1}{v2} = \frac {m2}{m1} = \frac {27}{1}$$ = 27:1.
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