(i) statement-I :- Large angle scattering of alpha Particle led to discovery of atomic nucleus. statement-II :- Entire Positive charge of atom is concentrated in the central core. (A) statement -I and II are true. and statement II is correct explanation of statement-I (B) statement -I and II are true, but statement-II is not correct explanation of statement I (C) statement I is true, but statement II is false. (D) statement I is false but statement II is true (ii) statement-I \(1 \mathrm{amu}=931.48 \mathrm{MeV}\) statement-II It follows form \(E=m c^{2}\) (iii) statement -I:- half life time of tritium is \(12.5\) years statement-II:- The fraction of tritium that remains after 50 years is \(6.25 \%\) (iv) statement-I:- Nuclei of different atoms have same size statement-II:- \(\mathrm{R}=\operatorname{Ro}(\mathrm{A})^{1 / 3}\)

Step by step solution

01

Verify Statement I

Rutherford's alpha particle scattering experiment led to the discovery of the atomic nucleus. This was due to large angle scattering of alpha particles. Thus, Statement I is true.

02

Verify Statement II

The atomic nucleus contains protons and neutrons, where protons carry the positive charge. The entire positive charge of an atom is indeed concentrated in its central core, which is the nucleus. Therefore, Statement II is true.

03

Analyze the relationship between the statements

Statement II provides the correct explanation for Statement I since it is due to the concentration of positive charge in the central core of the atom, the nucleus, that alpha particles experience large angle scattering. Hence, the correct answer is (A): Statement-I and II are true, and statement II is the correct explanation of statement-I. (ii)

04

Verify Statement I

One atomic mass unit (amu) is approximately equal to \(931.48 \mathrm{MeV}/c^2\), where \(c\) is the speed of light in a vacuum. Statement I correctly states the value of 1 amu.

05

Verify Statement II

Statement II claims that the energy-mass equivalence formula, Einstein's famous equation \(E=m c^{2}\), is what leads to the value of 1 amu in MeV. This is correct because when the mass of an atom is converted to energy, this equation is utilized.

06

Analyze the relationship between the statements

Statement II correctly explains the reason for Statement I being true. Thus, the correct answer is (A): Statement-I and II are true, and statement II is the correct explanation of statement-I. (iii)

07

Verify Statement I

The half-life of tritium (a radioactive isotope of hydrogen) is approximately 12.5 years. Statement I is accurate.

08

Verify Statement II

To find the fraction of tritium remaining after 50 years, we need to use the formula: \[ N = N_0 \left(\frac{1}{2}\right)^\frac{t}{t_{1/2}} \] Where \(N\) is the remaining amount, \(N_0\) is the initial amount, \(t\) is the elapsed time, and \(t_{1/2}\) is the half-life of a radioactive substance. Plugging in the values, we have \[ N = 1 \times \left(\frac{1}{2}\right)^\frac{50}{12.5} = 0.0625 \] which means that after 50 years, 6.25% of the tritium remains. Hence, Statement II is true.

09

Analyze the relationship between the statements

Statement II offers a correct explanation of the concept mentioned in Statement I since it demonstrates how much tritium remains at a specific point in time. Therefore, the correct answer is (A): Statement-I and II are true, and statement II is the correct explanation of statement-I. (iv)

10

Verify Statement I

The statement that nuclei of different atoms have the same size is incorrect. Nuclei size varies depending on the number of protons and neutrons.

11

Verify Statement II

The formula for the nuclear radius, \(\mathrm{R}=\operatorname{Ro}(\mathrm{A})^{1 / 3}\), where \(A\) is the mass number, and \(\operatorname{Ro}\) is a constant, supports that nuclei size varies depending on the mass number. Statement II is true.

12

Analyze the relationship between the statements

Statement I is false but Statement II is true. As a result, the correct answer is (D): statement I is false but statement II is true.

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