A nucleus has mass number α and radius R α R_{\alpha} R α . Another nucleus has mass number β and radius R β R_{\beta} R β . If β = 8α, then R α R β \frac{R_{\alpha}}{R_{\beta}} R β R α is :
Physics · Nuclear physics · Nuclear Properties, Mass Defect & Binding Energy
JEE Mains 2026 28 January Evening Shift

Question

A nucleus has mass number α and radius R α R_{\alpha} R α . Another nucleus has mass number β and radius R β R_{\beta} R β . If β = 8α, then R α R β \frac{R_{\alpha}}{R_{\beta}} R β R α is :

Physics · Nuclear physics · Nuclear Properties, Mass Defect & Binding Energy

JEE Mains 2026 28 January Evening Shift

G1 Physics · Accepted Answer

Nuclear radius is given by R = R₀A¹ᐟ³, where A is the mass number. Therefore, R(α) = R₀α¹ᐟ³, and R(β) = R₀β¹ᐟ³. Hence, R(α)/R(β) = (α/β)¹ᐟ³. Given, β = 8α. Therefore, R(α)/R(β) = (1/8)¹ᐟ³ = 1/2 = 0.5. Correct option: D.

A nucleus has mass number α and radius R α R_{\alpha} R α ​ . Another nucleus has mass number β and radius R β R_{\beta} R β ​ . If β = 8α, then R α R β \frac{R_{\alpha}}{R_{\beta}} R β ​ R α ​ ​ is :

A nucleus has mass number α and radius R α R_{\alpha} R α . Another nucleus has mass number β and radius R β R_{\beta} R β . If β = 8α, then R α R β \frac{R_{\alpha}}{R_{\beta}} R β R α is :