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Question: The ratio of the volume of the atom to the volume of the nucleus is of the order of...

The ratio of the volume of the atom to the volume of the nucleus is of the order of

A

1010

B

1015

C

1020

D

1025

Answer

1015

Explanation

Solution

Radius of the atom , Ra=1A苿˙蘂−10R_{a} = 1A\dot{苿}蘂^{- 10}

Volume of the atoms Va=43πRa3=43×π×(10−10)3m3V_{a} = \frac{4}{3}\pi R_{a}^{3} = \frac{4}{3} \times \pi \times (10^{- 10})^{3}m^{3}

Radius of the nucleus, Rn=1R_{n} = 1Fermi = 10−15m10^{- 15}m

Their corresponding ratio is

VaVn=(10−10)3(10−15)3=10−3010−45=1015\frac{V_{a}}{V_{n}} = \frac{(10^{- 10})^{3}}{(10^{- 15})^{3}} = \frac{10^{- 30}}{10^{- 45}} = 10^{15}