Chapter 11: Q16E (page 518)

Determine the approximate ratio of the diameter of a uranium nucleus $(A = 238)$ to that of beryllium nucleus $(A = 9)$

Short Answer

Expert verified

The ratio of the diameter of uranium nucleus to that of beryllium nucleus is $2.98$ .

Step by step solution

Given data

Mass number of Uranium nucleus $= 238$ .

Mass number of beryllium nucleus $= 9$ .

Formula of Radius of Uranium

The radius of uranium is given as, $r = A^{1 / 3} (R_{0})$ .

Here $A$ is the mass number and $R_{0}$ is a constant its value is $1 .2 \times 10^{- 15} m$ .

Calculation for the radius of uranium and beryllium

$9$ Substitute $9$ for mass number $A$ of uranium nucleus in the above equation.

$\begin{array}{l} r_{U} = A^{1 / 3} (R_{0}) \\ r_{U} = 238^{1 / 3} (R_{0}) \end{array}$

The radius of a beryllium nucleus is given as, $r_{B e} = A^{1 / 3} (R_{0})$ .

Substitutefor mass number $A$ of beryllium nucleus in the above equation.

$\begin{array}{l} r_{B e} = A^{1 / 3} (R_{0}) \\ r_{B e} = 9^{1 / 3} (R_{0}) \end{array}$

Calculation of the ration of the diameter

The ratio of the diameter of uranium nucleus to that of beryllium nucleus is given as, .

$\frac{D_{U J}}{D_{B_{e}}} = \frac{2 (r_{U J})}{2 (r_{B_{e} e})}$

Substitute $238^{1 / 3} (R_{0})$ for $r_{U}$ and $9^{1 / 3} (R_{0})$ for $r_{B e}$ in the above equation.

$\begin{matrix} \frac{D_{u}}{D_{z e}} = \frac{2 (r_{l})}{2 (r_{R_{k}})} \\ \frac{D_{u}}{D_{z e}} = \frac{2 (238^{1 / 3} R_{0})}{2 (9^{1 / 3} R_{0})} \\ \frac{D_{u}}{D_{z e}} = 2.98 \end{matrix}$

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Determine the approximate ratio of the diameter of a uranium nucleus $(A = 238)$ to that of beryllium nucleus $(A = 9)$

Short Answer

Step by step solution

Given data

Formula of Radius of Uranium

Calculation for the radius of uranium and beryllium

Calculation of the ration of the diameter

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Determine the approximate ratio of the diameter of a uranium nucleus (A=238)to that of beryllium nucleus(A=9)

Short Answer

Step by step solution

Given data

Formula of Radius of Uranium

Calculation for the radius of uranium and beryllium

Calculation of the ration of the diameter

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Electricity and Magnetism

Electrostatics

Torque and Rotational Motion

Rotational Dynamics

Force

Study anywhere. Anytime. Across all devices.

Determine the approximate ratio of the diameter of a uranium nucleus $(A = 238)$ to that of beryllium nucleus $(A = 9)$