Question

which of the following statement is true (A) \({ }_{78} \mathrm{Pt}^{192}\) has 78 neutrons (B) \({ }_{90} \mathrm{Th}^{234} \rightarrow{ }_{91} \mathrm{~Pa}^{234}+{ }_{2} \mathrm{He}^{4}\) (C) \({ }_{92} \mathrm{U}^{238} \rightarrow{ }_{90} \mathrm{Th}^{234}+{ }_{2} \mathrm{He}^{4}\) (D) \({ }_{84} \mathrm{Po}^{214} \rightarrow{ }_{82} \mathrm{~Pb}^{210}+\beta^{-}\)

Short answer

The correct statement is (C): \({ }_{92} \mathrm{U}^{238} \rightarrow{ }_{90} \mathrm{Th}^{234}+{ }_{2}\mathrm{He}^{4}\).

Step-by-step solution

Statement A: Number of neutrons in \({ }_{78} \mathrm{Pt}^{192}\)

The notation for this isotope of platinum is given by \({ }_{Z} \mathrm{Pt}^{A}\) where A is the mass number (total number of protons and neutrons) and Z is the atomic number (number of protons). To find the number of neutrons, we can use the formula: Number of neutrons = A - Z Now we have: Number of neutrons = 192 - 78 Number of neutrons = 114 Since the statement claims that this isotope has 78 neutrons, statement (A) is false.

Statement B: Nuclear reaction \({ }_{90} \mathrm{Th}^{234} \rightarrow{ }_{91} \mathrm{~Pa}^{234}+{ }_{2}\mathrm{He}^{4}\)

To verify whether this nuclear equation is balanced, we should compare the sum of mass numbers and the sum of atomic numbers on both sides of the reaction. Left side: atomic number = 90, mass number = 234 Right side: atomic number = 91 + 2 = 93, mass number = 234 + 4 = 238 This nuclear reaction is not balanced, so statement (B) is false.

Statement C: Nuclear reaction \({ }_{92} \mathrm{U}^{238} \rightarrow{ }_{90} \mathrm{Th}^{234}+{ }_{2}\mathrm{He}^{4}\)

Similarly, let's check if this nuclear reaction is balanced: Left side: atomic number = 92, mass number = 238 Right side: atomic number = 90 + 2 = 92, mass number = 234 + 4 = 238 Both the atomic numbers and mass numbers are equal on both sides of the reaction, indicating that this nuclear reaction is balanced. Statement (C) is true.

Statement D: Nuclear reaction \({ }_{84} \mathrm{Po}^{214} \rightarrow{ }_{82}\mathrm{~Pb}^{210}+\beta^{-}\)

Let's verify if this nuclear reaction is balanced: Left side: atomic number = 84, mass number = 214 Right side: atomic number = 82 + (-1) = 81 (since a beta particle has a charge of -1), mass number = 210 + 0 = 210 (a beta particle has negligible mass) The atomic numbers and mass numbers are not equal on both sides of the reaction, so statement (D) is false. #Conclusion# Among the given statements, only statement (C) is true: \({ }_{92} \mathrm{U}^{238} \rightarrow{ }_{90} \mathrm{Th}^{234}+{ }_{2}\mathrm{He}^{4}\).

Key concepts

Mass Number

When discussing nuclear reactions, the mass number plays a crucial role. It represents the total number of protons and neutrons in an atom's nucleus. The mass number is often symbolized by the letter "A" and appears as a superscript in nuclear notation. For example, in the isotope \( {}_{92} \mathrm{U}^{238} \), 238 represents the mass number.

This sum is essential because it allows us to determine the overall size of a nucleus and helps identify different isotopes of elements. Calculating the mass number also helps in balancing nuclear equations, where this sum must be equal on both sides of the reaction. Keeping an eye on mass number changes can give insights into particles lost or gained in transformations.

Atomic Number

The atomic number is a fundamental concept in understanding atomic structure and nuclear reactions. It is the number of protons in an atom's nucleus and is denoted by "Z." In a nuclear symbol like \( {}_{78} \mathrm{Pt}^{192} \), 78 represents the atomic number, determining the element type.

The atomic number uniquely identifies each element on the periodic table, as no two different elements will have the same atomic number. In nuclear reactions, just like the mass number, the total atomic number must be the same on both sides to maintain balance.

• It tells us about the element's identity.
• The atomic number directly relates to the element's position in the periodic table.
• Changes in the atomic number indicate transmutation into different elements.

Understanding atomic number shifts during reactions is vital for comprehending the nature of nuclear processes.

Balanced Nuclear Equation

A balanced nuclear equation is critical in ensuring the conservation of mass and charge during nuclear reactions. The balance takes into account that both the combined mass number and atomic number of reactants and products must be equal.

For instance, in the reaction \( {}_{92} \mathrm{U}^{238} \rightarrow {}_{90} \mathrm{Th}^{234} + {}_{2} \mathrm{He}^{4} \), both the atomic and mass numbers balance:

• Atomic Numbers: 92 (left side) = 90 + 2 (right side)
• Mass Numbers: 238 (left side) = 234 + 4 (right side)

When properly written and balanced, these equations help effectively describe the changes occurring during transformations. They offer a straightforward way of understanding particle gain or loss, as well as element transformation.

Neutron Calculation

Neutron calculation is a straightforward process but crucial for understanding the composition of an atom's nucleus. Neutrons are the particles in the nucleus without a charge, and to find the number of neutrons in an atom, you subtract the atomic number from the mass number:

Neutrons = Mass Number (A) - Atomic Number (Z).

For example, in \( {}_{78} \mathrm{Pt}^{192} \), the number of neutrons can be calculated by:
- Mass Number = 192
- Atomic Number = 78
- Neutrons = 192 - 78 = 114

This approach is useful not only for identifying isotopes but also for predicting the stability of atomic nuclei. A typical usage here is to identify whether nuclei are more likely to undergo radioactive decay based on their neutron number.