Verified Solution • 2025–26 Session moderate

QJEEM20Ph7d4b: JEE Main 2020 Physics - Class 12 JEEM20Ph7d4b Solution: The radius R of a nucleus of mass number A can be estimated by…

The radius R of a nucleus of mass number A can be estimated by the formula
R = (1.3 ×\times 10–15)A1/3 m.
It follows that the mass density of a nucleus is of the order of :

(Mprot. ≅\cong Mneut ≃\simeq 1.67 ×\times 10–27 kg)

Multiple Choice Options

  • A 1024 kg m–3
  • B 1010 kg m–3
  • C 1017 kg m–3
  • D 103 kg m–3

Step-by-Step Verified Solution

R=(1.3×10−15)A13R = (1.3 \times {10^{ - 15}}){A^{{1 \over 3}}}

We know, m=pVm = pV

⇒\Rightarrow p=mVp = {m \over V}

⇒\Rightarrow p=mpA43πR3p = {{{m_p}A} \over {{4 \over 3}\pi {R^3}}}

p=mpA43π×(1.3×10−15)3Ap = {{{m_p}A} \over {{4 \over 3}\pi \times {{(1.3 \times {{10}^{ - 15}})}^3}A}}

p≈1017kg/mp \approx {10^{17}}kg/m

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