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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 binding energy Per nucleon of deuteron $\left({ }^{2}{ }_{1} \mathrm{H}\right)\( and Lielium nucleus \){ }_{2}{ }^{4}{ }_{2} \mathrm{He}$ ) is \(1.1 \mathrm{MeV}\) and \(7.0 \mathrm{MeV}\). respectively. If two deuteron react to form a single helium nucleus, the energy released is (A) \(23.6 \mathrm{MeV}\) (B) \(26.9 \mathrm{MeV}\) (C) \(13.9 \mathrm{MeV}\) (D) \(19.2 \mathrm{MeV}\)

In the following disintegration series ${ }_{92} \mathrm{U}^{238} \rightarrow^{\alpha} \mathrm{x} \rightarrow^{\beta-}{ } \mathrm{Z} \mathrm{y}^{\mathrm{A}}$ The value of \(Z\) and \(A\) respectively will be (A) 90,234 (B) 92,236 (C) 88,234 (D) 91,234

The energy difference between the first two levels of hydrogen atom is $10.2 \mathrm{eV}$. what is the corresponding energy difference for a singly ionized helium atom? (A) \(10.2 \mathrm{eV}\) (B) \(81.6 \mathrm{eV}\) (C) \(20.4 \mathrm{eV}\) (D) \(40.8 \mathrm{eV}\)

If \(\mathrm{M}_{0}\) is the mass of an isotope, ${ }^{17}{ }_{8} \mathrm{O}, \mathrm{M}_{\mathrm{p}}\( and \)\mathrm{M}_{\mathrm{n}}$ are the masses of a Proton and neutron respectively, the binding energy of the isotope is (A) \(\left(\mathrm{M}_{0}-8 \mathrm{M}_{\mathrm{p}}\right) \mathrm{C}^{2}\) (B) $\left(\mathrm{M}_{0}-8 \mathrm{M}_{p}-9 \mathrm{M}_{\mathrm{n}}\right) \mathrm{C}^{2}$ (C) \(\left(\mathrm{M}_{0}-17 \mathrm{M}_{\mathrm{n}}\right) \mathrm{C}^{2}\) (D) \(\mathrm{M}_{\mathrm{O}} \mathrm{C}^{2}\)

Read the following question and choose correct Answer form given below. (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion. (B) Both assertion and reason are true. Reason is not correct explanation of the assertion. (C) Assertion is true but reason is false. (D) Assertion is false and Reason are true. (i) Assertion :- In a radio-active disintegration, an electron is emitted by nucleus. Reason :- electron are always Present in-side the nucleus. (ii) Assertion :- An electron and Positron can annihilate each other creating Photon Reason:- Electron and Positron form a Particle and anti Particle pair. (iii) Assertion:- An isolated radioactive atom may not decay at all what ever be its half time Reason:- Radioactive decay is a statistical Phenomena. (iv) Assertion:- Fragment Produced in the fission of \(\mathrm{u}^{235}\) are active Reason:- The fragments have abnormally high Proton to neutron ratio
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