Problem 68 - Master Resource Book in JEE Main Physics

Question

\({ }_{92} \mathrm{U}^{235}\) and \({ }_{92} \mathrm{U}^{238}\) differ as (a) \({ }_{92} \mathrm{U}^{235}\) has 2 protons less (b) \({ }_{92} \mathrm{U}^{238}\) has 3 protons more (c) \({ }_{92} \mathrm{U}^{238}\) has 3 neutrons more (d) None of the above

Step-by-Step Solution

Answer

(c) \({ }_{92} \mathrm{U}^{238}\) has 3 neutrons more

Step 1: Identify the given isotopes

We have two isotopes of Uranium provided: \({ }_{92} \mathrm{U}^{235}\) and \({ }_{92} \mathrm{U}^{238}\). Both isotopes have the same number of protons because they are isotopes of the same element.

Step 2: Determine the number of protons

For any uranium isotope, the atomic number is 92, which represents the number of protons. Therefore, both \( { }_{92} \mathrm{U}^{235} \) and \( { }_{92} \mathrm{U}^{238} \) have 92 protons.

Step 3: Calculate the number of neutrons

Neutrons are determined by subtracting the number of protons from the mass number. For \( { }_{92} \mathrm{U}^{235} \), neutrons = \( 235 - 92 = 143 \). For \( { }_{92} \mathrm{U}^{238} \), neutrons = \( 238 - 92 = 146 \).

Step 4: Compare the number of neutrons

We find that \( { }_{92} \mathrm{U}^{238} \) has 146 neutrons and \( { }_{92} \mathrm{U}^{235} \) has 143 neutrons. Therefore, \( { }_{92} \mathrm{U}^{238} \) has 3 more neutrons than \( { }_{92} \mathrm{U}^{235} \).

Key Concepts

Understanding Uranium Isotopes

Uranium isotopes such as \( { }_{92} \mathrm{U}^{235} \) and \( { }_{92} \mathrm{U}^{238} \) are variants of the element uranium.These isotopes have the same atomic number but different mass numbers.The atomic number is 92 for uranium, indicating the number of protons, whereas the mass number differs because of the varying number of neutrons.

• \( { }_{92} \mathrm{U}^{235} \) is known for its use in nuclear reactors and weapons due to its ability to sustain a fission chain reaction.
• \( { }_{92} \mathrm{U}^{238} \), while plentiful, is not fissile but can be converted into \( { }_{94} \mathrm{Pu}^{239} \), a fissile material.

To understand isotopes more fully, consider them as family members with the same last name (protons) but different middle names (neutrons).
They behave similarly chemically but differ in nuclear properties.

Exploring Atomic Structure and Its Significance

Atomic structure is central to understanding isotopes and elemental behavior in chemistry. Every atom consists of protons, neutrons, and electrons.

• Protons are positively charged particles located in the atomic nucleus.
• Neutrons, which have no charge, also reside in the nucleus.
• Electrons are negatively charged and orbit the nucleus.

The number of protons (atomic number) defines the element’s identity, while the sum of protons and neutrons (mass number) defines the isotope of the element. For example, in uranium, the atomic number is 92, indicating 92 protons.
The mass number tells us how many total particles are in the nucleus, guiding our understanding of isotopic characteristics.

Neutron Calculation Simplified

Calculating the number of neutrons is straightforward and pivotal for distinguishing between isotopes.Neutrons add to the atomic mass and affect nuclear properties, like stability.
Here's how to calculate the number of neutrons:

• Identify the mass number, which is the upper number often denoted at the top left of the element symbol.
• Subtract the atomic number (number of protons) from the mass number.

For instance, for \( { }_{92} \mathrm{U}^{235} \), you subtract 92 from 235, yielding 143 neutrons.And for \( { }_{92} \mathrm{U}^{238} \), subtracting 92 from 238 gives 146 neutrons.
This calculation highlights that \( { }_{92} \mathrm{U}^{238} \) has 3 MORE neutrons than \( { }_{92} \mathrm{U}^{235} \), which is crucial information in identifying isotopic differences clearly.