JEE Main 2022 · 25 June · evening · Single correct · +4 / −1

Which of the following figure represents the variation of lₙ( R/R₀ ) with lₙA (if R = radius of a nucleus and A = its mass number)

  1. (a)
    Option (a)
  2. (b)
    Option (b)
  3. (c)
    Option (c)
  4. (d)
    Option (d)
Answer and solution

Answer (b)

Solution

Physics sir · 4 steps

Take log of both sides of R = R₀A^(1/3) and the power law becomes a straight line.

  1. Size of a nucleus. The radius of a nucleus grows with its mass number as R = R₀ A^(1/3), where R₀ ≈ 1.2 fm is a constant.
  2. Take logarithms. Divide by R₀ and take the natural log of both sides. The power 1/3 comes down as a plain multiplier.

    ln(R/R₀) = 1/3 ln A

  3. Read the graph. This has the form y = mx with y = ln(R/R₀), x = ln A and m = 1/3. So the plot is a straight line with a positive slope, heading through the origin. It does not bend up, bend over, or fall.
  4. So. Only figure (b) shows a rising straight line, so the answer is (b).

The idea to keep. Any power law y = kxⁿ plotted as ln y against ln x gives a straight line of slope n. Spot the power, and the log-log graph is always a line.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Nuclear Physics

Asked about 110 times in JEE Main since 2020. This question is from 2022.