Question

\(\Lambda\) boron carbide rod is used in a nuclear reactor because \(\left({ }^{10} \mathrm{~B}\right)\) has very (1) low cross-scctional area for capturing neutrons. (2) high cross-sectional arca for capturing neutrons. (3) low cross-scctional area for removing positrons. (4) high cross-sectional area for capturing neutrions.

Short answer

(2) high cross-sectional area for capturing neutrons.

Step-by-step solution

- Understand the Concept of Cross-Sectional Area

The cross-sectional area in nuclear physics refers to the likelihood of a nuclear reaction taking place between a target nucleus and an incident particle such as a neutron. A higher cross-sectional area means the probability of the reaction occurring is greater.

- Identify the Element and Isotope

The problem mentions boron carbide used in nuclear reactors and specifically references the isotope \(^10\mathrm{~B}\). This isotope is known for its properties in capturing neutrons.

- Determine the Relevant Physical Property

In nuclear reactors, materials effective in capturing neutrons are desired as they help to control the reaction. Boron-10 (\(^10\mathrm{~B}\)) is known to have a very high probability of capturing neutrons, which is desired for controlling nuclear reactions.

- Match the Property with Given Options

Compare the identified property with the provided answer choices. From the analysis, the correct choice is the one that describes a high cross-sectional area for capturing neutrons.

Key concepts

Cross-Sectional Area

The cross-sectional area in nuclear physics is a vital concept. It refers to how likely a nuclear reaction will happen between a target nucleus and an incoming particle, like a neutron. Imagine it as target practice: the larger the target, the easier it is to hit. In this context, a larger cross-sectional area means a higher chance for the neutron to interact with the nucleus.
An important aspect of this concept includes:

• If a material has a high cross-sectional area for neutron capture, it means that it is very effective at capturing neutrons.


• In nuclear reactors, this property is crucial. Control rods made from materials with a high cross-sectional area can slow down or stop the reaction by capturing excess neutrons.

In summary, understanding cross-sectional area helps us grasp how materials interact with particles in nuclear settings.

Neutron Capture

Neutron capture is a process where an atomic nucleus absorbs a neutron.
This process is essential in controlling nuclear reactions, as it can stabilize or affect the chain reactions within a reactor.

• Materials that capture neutrons effectively are used in control rods to manage the reaction.


• When neutrons are captured, they reduce the number of free neutrons that can continue the reaction.

The process of neutron capture is pivotal in ensuring that nuclear reactions happen safely and effectively.

Boron-10 Isotope

Boron-10 (^{10}B) is a specific isotope of the element boron that is particularly useful in nuclear reactors. Here's why it is so significant:

• Boron-10 has a high cross-sectional area for neutron capture, making it very efficient at absorbing neutrons.


• This property is exploited in nuclear reactors for controlling the nuclear reaction.


• When boron-10 captures a neutron, it often transforms into boron-11, a stable isotope, without emitting dangerous radiation.

In summary, ^{10}B is a star player in nuclear reactors, ensuring the reactions are kept under control and safe for operation.