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Q16E

Expert-verified
Modern Physics
Found in: Page 518
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

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

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

See the step by step solution

Step by Step Solution

Step 1: Given data

Mass number of Uranium nucleus =238.

Mass number of beryllium nucleus =9.

Step 2: Formula of Radius of Uranium

The radius of uranium is given as, r=A1/3(R0).

Here A is the mass number and R0 is a constant its value is 1.2×1015 m.

Step 3: Calculation for the radius of uranium and beryllium

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

rU=A1/3(R0)rU=2381/3(R0)

The radius of a beryllium nucleus is given as, rBe=A1/3(R0) .

Substitute for mass number A of beryllium nucleus in the above equation.

rBe=A1/3(R0)rBe=91/3(R0)

Step 4: Calculation of the ration of the diameter

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

DUJDBe=2(rUJ)2(rBee)

Substitute 2381/3(R0) for rU and 91/3(R0) for rBe in the above equation.

DuDze=2(rl)2(rRk)DuDze=2(2381/3R0)2(91/3R0)DuDze=2.98

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