Question

Read the following question and choose correct Answer form given below. (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion. (B) Both assertion and reason are true. Reason is not correct explanation of the assertion. (C) Assertion is true but reason is false. (D) Assertion is false and Reason are true. (i) Assertion :- In a radio-active disintegration, an electron is emitted by nucleus. Reason :- electron are always Present in-side the nucleus. (ii) Assertion :- An electron and Positron can annihilate each other creating Photon Reason:- Electron and Positron form a Particle and anti Particle pair. (iii) Assertion:- An isolated radioactive atom may not decay at all what ever be its half time Reason:- Radioactive decay is a statistical Phenomena. (iv) Assertion:- Fragment Produced in the fission of \(\mathrm{u}^{235}\) are active Reason:- The fragments have abnormally high Proton to neutron ratio

Short answer

(i) (C) Assertion is true but reason is false. (ii) (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion. (iii) (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion. (iv) (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion.

Step-by-step solution

Assertion 1 and Reason 1

The assertion mentions that in a radioactive disintegration, an electron is emitted by the nucleus. This is correct. The given reason for this is that electrons are always present inside the nucleus. This reason is incorrect, as electrons are not usually found inside the nucleus. So the correct answer for this pair is: (C) Assertion is true but reason is false.

Assertion 2 and Reason 2

The assertion states that an electron and positron can annihilate each other, creating a photon. This is a correct statement. The reason given is that an electron and positron form a particle and antiparticle pair. This reason is also true and it correctly explains the phenomenon of annihilation between electron and positron. So the correct answer for this pair is: (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion.

Assertion 3 and Reason 3

The assertion states that an isolated radioactive atom may not decay at all, regardless of its half-life. This statement is true because radioactive decay is a probabilistic event, and it's possible that an individual atom might never decay. The given reason for this is that radioactive decay is a statistical phenomenon. This reason is also true, and it provides the correct explanation for the assertion. So the correct answer for this pair is: (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion.

Assertion 4 and Reason 4

The assertion states that fragments produced in the fission of \(\mathrm{U}^{235}\) are active. This is true because the fission fragments resulting from the splitting of the uranium nucleus are radioactive isotopes. The given reason for this is that the fragments have an abnormally high proton-to-neutron ratio. This is also true, as the high proton-to-neutron ratio leads to an unstable nucleus, making the fragments radioactive. So the correct answer for this pair is: (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion.

Key concepts

Particle-antiparticle Annihilation

When particles and their corresponding antiparticles meet, they can undergo a process called annihilation. A classical example of this is when an electron and its antiparticle, a positron, collide. As a result of this particle-antiparticle interaction, they both transform into energy in the form of photons. This is due to the fundamental principle of energy conservation where the mass of both particles is converted into energy. The photon, a particle of light, is the typical product of such an annihilation event.

The electron-positron annihilation is a clear illustration of the relationship between mass and energy, famously described by Albert Einstein's equation, \( E=mc^2 \). Here, \(m\) is the mass lost during the collision and \(c\) is the speed of light. This equates the mass disappearing during annihilation to a measurable quantity of energy, released as photons.

• Annihilation results in the formation of photons.
• It exemplifies Einstein's principle of mass-energy equivalence.
• The process underscores the relationship between particles and antiparticles.

Radioactive Isotopes

Radioactive isotopes, often referred to as radioisotopes, are isotopes of elements that exhibit radioactivity due to an unstable nucleus. These isotopes have extra neutrons compared to stable isotopes, which leads to the emission of particles as they seek stability. During this decay, radiation is emitted, which can include alpha particles, beta particles, or gamma rays.

The activity of these isotopes is characterized by their half-life, which is the time taken for half of the radioactive atoms in a sample to decay. The phenomenon is integral to many applications, ranging from medical treatments in radiotherapy to carbon dating techniques in archaeology. The key is understanding how these isotopes behave and their role in various scientific and medical fields.

• Radioisotopes have unstable atomic structures prone to decay.
• This instability results in the release of radiation.
• They are crucial in fields like medicine and archaeology.

Statistical Phenomena in Radioactivity

Radioactive decay isn't deterministic for individual atoms. It's best understood as a statistical process. This means, while the decay can be predicted for a large population of radioactive atoms, predicting when a particular next atom will decay is impossible.

This statistical nature arises from quantum mechanics. Each atom has a probability of decaying within a certain time period, defined by its half-life, but no certainty. Therefore, an isolated radioactive atom could theoretically remain undecayed forever, highlighting the probabilistic nature of radioactive events.

• Decay in radioactivity is probabilistic, not certain.
• Quantum mechanics plays a central role in defining decay probability.
• A half-life defines the time frame, but not the certainty, of decay events.