The radius of atom is of the order of 1 Å and radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?

The correct option is 10¹⁵.

To find how many orders of magnitude higher the volume of an atom is compared to the volume of its nucleus, we can determine the ratio of their volumes based on their respective radii.

First, let's write down the given radii in meters:
Radius of the atom (R_atom) = 1 Å = 10^-10 m
Radius of the nucleus (R_nucleus) = 1 fermi = 10^-15 m

Assuming both the atom and the nucleus to be spherical in shape, the volume (V) of a sphere is given by the formula:
$$V=\frac{4}{3}\pi R^3$$

Now, let's calculate the ratio of the volume of the atom to the volume of the nucleus:
$$\frac{V_{\text{atom}}}{V_{\text{nucleus}}}=\frac{\frac{4}{3}\pi R_{\text{atom}}^3}{\frac{4}{3}\pi R_{\text{nucleus}}^3}={(\frac{R_{\text{atom}}}{R_{\text{nucleus}}}}^3$$

Substitute the values of the radii into the equation:
$$\frac{V_{\text{atom}}}{V_{\text{nucleus}}}={\left(\frac{{10}^{-10}}{{10}^{-15}}\right)}^3$$

Simplify the fraction inside the parentheses by subtracting the exponents:

Now, raise this result to the power of 3:
$$\frac{V_{\text{atom}}}{V_{\text{nucleus}}}={\left({10}^5\right)}^3={10}^{15}$$

Therefore, the volume of the atom is 10¹⁵ magnitudes higher than the volume of the nucleus.