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