A nucleus has mass number and radius R . Another nucleus has mass number and radius R . If = 8 then R / R is : [2026]

Question

A nucleus has mass number $α$ and radius $R_{α}$ . Another nucleus has mass number $β$ and radius $R_{β}$ . If $β = 8 α$ then $R_{α} / R_{β}$ is : [2026]

Smart Achievers · Accepted Answer

(2)

$R_{α} = R_{0} α^{1 / 3}$

$R_{β} = R_{0} β^{1 / 3}$

$\frac{R_{α}}{R_{β}} = {(\frac{α}{β})}^{1 / 3} = \frac{1}{2}$

Solution

Q.
A nucleus has mass number $α$ and radius $R_{α}$ . Another nucleus has mass number $β$ and radius $R_{β}$ . If $β = 8 α$ then $R_{α} / R_{β}$ is : [2026]

1 1

2 0.5

3 2

4 8

Ans.
(2)

$R_{α} = R_{0} α^{1 / 3}$

$R_{β} = R_{0} β^{1 / 3}$

$\frac{R_{α}}{R_{β}} = {(\frac{α}{β})}^{1 / 3} = \frac{1}{2}$

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Solution

Q. A nucleus has mass number α and radius Rα. Another nucleus has mass number β and radius Rβ. If β=8α then Rα/Rβ is : [2026]

1 1

2 0.5

3 2

4 8

Ans. (2) Rα=R0α1/3 Rβ=R0β1/3 RαRβ=(αβ)1/3=12

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Q.
A nucleus has mass number $α$ and radius $R_{α}$ . Another nucleus has mass number $β$ and radius $R_{β}$ . If $β = 8 α$ then $R_{α} / R_{β}$ is : [2026]

Ans.
(2)

$R_{α} = R_{0} α^{1 / 3}$

$R_{β} = R_{0} β^{1 / 3}$

$\frac{R_{α}}{R_{β}} = {(\frac{α}{β})}^{1 / 3} = \frac{1}{2}$