Question 5 of 13beginner🔧 ApplyNumerical2 marks

Obtain approximately the ratio of the nuclear radii of the gold isotope 79197Au^{197}_{79}\text{Au} and the silver isotope 47107Ag^{107}_{47}\text{Ag}.

Correct Answer

The ratio of the nuclear radii of gold isotope to silver isotope is approximately 1.22.

Exercise: EXERCISES | Q: 13.4 | (Chapter: 16)
For More Understanding

Explanation

This question tests the application of the nuclear radius formula R = R₀A^(1/3). The key insight is that R₀ is a constant that cancels out when taking the ratio, so only the mass numbers matter. Students should recognize that the ratio depends solely on the cube root of the mass numbers.

Solution Steps

  1. Step 1: Write the formula for nuclear radius from the context: R = R₀A^(1/3), where A is the mass number.

  2. Step 2: For gold isotope ¹⁹⁷Au, mass number A₁ = 197. For silver isotope ¹⁰⁷Ag, mass number A₂ = 107.

  3. Step 3: Calculate the ratio: R₁/R₂ = (R₀ × 197^(1/3))/(R₀ × 107^(1/3)) = (197/107)^(1/3).

  4. Step 4: Compute: 197/107 ≈\approx 1.841, and (1.841)^(1/3) ≈\approx 1.22.

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