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NEET PHYSICSNUCLEIMedium

Question

If the nuclear radius of 27Al^{27}\text{Al} is 3.6 Fermi, the approximate nuclear radius of 64Cu^{64}\text{Cu} in Fermi is:

A

2.4

B

1.2

C

4.8

D

3.6

Step-by-Step Solution

  1. Formula: The nuclear radius (RR) is related to the mass number (AA) by the empirical formula: R=R0A1/3R = R_0 A^{1/3} where R0R_0 is a constant (1.2 fm1.2 \text{ fm}).
  2. Set up Ratio: comparing the radii of Copper (Cu) and Aluminum (Al): RCuRAl=R0(ACu)1/3R0(AAl)1/3=(ACuAAl)1/3\frac{R_{\text{Cu}}}{R_{\text{Al}}} = \frac{R_0 (A_{\text{Cu}})^{1/3}}{R_0 (A_{\text{Al}})^{1/3}} = \left( \frac{A_{\text{Cu}}}{A_{\text{Al}}} \right)^{1/3}
  3. Substitution: Given AAl=27A_{\text{Al}} = 27, RAl=3.6 fmR_{\text{Al}} = 3.6 \text{ fm}, and ACu=64A_{\text{Cu}} = 64: RCu3.6=(6427)1/3\frac{R_{\text{Cu}}}{3.6} = \left( \frac{64}{27} \right)^{1/3}
  4. Calculation: (6427)1/3=(43)1/3(33)1/3=43\left( \frac{64}{27} \right)^{1/3} = \frac{(4^3)^{1/3}}{(3^3)^{1/3}} = \frac{4}{3} RCu=3.6×43=1.2×4=4.8 fmR_{\text{Cu}} = 3.6 \times \frac{4}{3} = 1.2 \times 4 = 4.8 \text{ fm}
  5. Conclusion: The nuclear radius of 64Cu^{64}\text{Cu} is approximately 4.8 Fermi.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from NUCLEI. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSNUCLEInuclearradiustextalapproximatenuclear

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