Question

The volume of nucleus is smaller than that of the
atom by a factor of about
(a) 10
(b) 10 5 Heid
(c) 10 10
(d)10 15​

Answer 1

Explanation:

Experiments on scattering of a-particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about 104. This means the volume of a nucleus is about 10–12 times the volume of the atom. In other words, an atom is almost empty.

Volume fraction = Volumeofnucleus / Totalvol.ofatom

= (4/3)π(10 ^−13 ) ^3 / (4/3)π(10 ^−8 )^3

=10^5

So, the corret answer is 10^5

So, the corret answer is 10^5

Answer 2

• As per the data given in the above question.
• To find the volume of an atom to the volume of the nucleus.

Let us consider

$The \: radius \: of \: the \: atom (r_1) = {10}^{ - 10}$

$The \: radius\: of \: the \: nucleus(r_2)={10}^{ - 15}$

Let us take the volume of the atom to the volume of the nucleus, then we get

$volume \: of \: sphere \: is \frac{4}{3} \pi {r}^{3}$

so,

$\frac{volume \: of \: atom }{volume \: of \: nucleus} = \frac{ \frac{4}{3} \pi \: r_1 }{ \frac{4}{3} \pi \: r_2}$

$\frac{volume \: of \: atom }{volume \: of \: nucleus} = \frac{ {({10}^{ - 10}) }^{3} }{ ( {{10}^{ - 15} )}^{3} }$

$\frac{volume \: of \: atom }{volume \: of \: nucleus} = \frac{ {10}^{ - 30} }{ {10}^{ - 45} }$

shift the power because the base is same,

$\frac{volume \: of \: atom }{volume \: of \: nucleus} = {10}^{( - 30 + 45)}$

$\frac{volume \: of \: atom }{volume \: of \: nucleus} = {10}^{15}$

Hence,

The ratio of the volume of an atom to the volume of the nucleus is 10¹⁵.

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