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Chapter 18: Problem 2477

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

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

Step by step solution

01

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.
02

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.
03

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.
04

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

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Most popular questions from this chapter

The Probability of survival of a radioactive nucleus for one mean life time is (A) \(1-(1 / \mathrm{e}) \mathrm{S}\) (B) \((1 / \mathrm{e})\) (C) \((2 / \mathrm{e})\) (D) \((3 / \mathrm{e})\)

A nucleus with \(\mathrm{Z}=92\) emits the following sequence $\alpha, \alpha, \beta^{-}\( \)\beta^{-}, \alpha, \alpha, \alpha, \alpha, \beta^{-}, \beta^{-}, \alpha, \beta^{+}, \beta^{+}, \alpha\( The \)\mathrm{Z}$ of the resulting nucleus is (A) 76 (B) 78 (C) 74 (D) 82

Match column I and II and chose correct Answer form the given below. (a) Nuclear fusion (p) converts some matter into energy (b) Nuclear fission (q) generally Possible for nuclei with low atomic number (c) \(\beta\) decay (r) generally Possible for nuclei with high atomic number (d) Exothermic nuclear (s) Essentially Proceeds by weak reaction nuclear force(c) (A) $\mathrm{a} \rightarrow \mathrm{p}, \mathrm{b} \rightarrow \mathrm{r}, \mathrm{c} \rightarrow \mathrm{s}, \mathrm{d} \rightarrow \mathrm{q}$ (B) $\mathrm{a} \rightarrow \mathrm{q}, \mathrm{b} \rightarrow \mathrm{r}, \mathrm{c} \rightarrow \mathrm{p}, \mathrm{d} \rightarrow \mathrm{s}$ (C) $\mathrm{a} \rightarrow \mathrm{q}, \mathrm{b} \rightarrow \mathrm{r}, \mathrm{c} \rightarrow \mathrm{s}, \mathrm{d} \rightarrow \mathrm{p}$ (D) $\mathrm{a} \rightarrow \mathrm{r}, \mathrm{b} \rightarrow \mathrm{q}, \mathrm{c} \rightarrow \mathrm{p}, \mathrm{d} \rightarrow \mathrm{s}$

The ionization Potential of hydrogen atom is \(13.6 \mathrm{eV}\). An electron in the ground state absorbs Photon of energy \(12.75 \mathrm{eV}\). How many different spectral lines can one expect when electron make a down ward transition (A) 1 (B) 2 (C) 6 (D) 4

The radius of Ge nucleus is measured to be twice the radius of ${ }^{9}{ }_{4}$ Be. The number of nucleons in Ge are (A) 72 (B) 78 (C) 65 (D) 80
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