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The radius of germanium nuclide is measured to be twice the radius of ₄⁹Be. The number of nucleons in Ge are
Options
(a) 72
(b) 73
(c) 74
(d) 75
Correct Answer:
72
Explanation:
Nuclear radii R = R₀(A)¹/³, where R₀ = 1.2 Fm
(or), R ∝ (A)¹/³
Rʙₑ / Rɢₑ = (9)¹/³ / (A)¹/³ (or), Rʙₑ / 2Rʙₑ = (9)¹/³ / (A)¹/³ (Given: Rɢₑ = 2Rʙₑ)
(A)¹/³ = 2 × (9)¹/³ ⇒ A = 2³ × 9 = 8 × 9 = 72
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Nuclear Radius, R=Ro(A)1/3, where Ro ~ 1.2fm (fermi unit=10-15)
Or R=(A)1/3.
RBe /RGe = (9)1/3/(A)1/3
RBe /2 RBe = (9)1/3/(A)1/3 …-(Given: RBe: RGe = 1:2)
Or (A)1/3 = 2*(9)1/3
Hence, A=23 * 9
=8*9
=72.
Hence, the number of nucleons is 72.