Question

The radius of an atom is of the order of 1Aº & the radius of
The nucleus is of the order of fermi. How many magnitudes
higher is the volume of the atom as compared to the
volume of the nucleus?
State the number of significant figures in
(i) 0.007 m2 (ii) 2.64 × 10 24 kg
(iii) 0.2370 g cm–3 (iv) 0.2300m
(v) 86400 (vi) 86400 m

Answer 1

I.)

Given:

• The radius of an atom is of the order of 1Aº.
• The radius of the nucleus is of the order of fermi.

To find:

• How many magnitudes higher is the volume of the atom as compared to the volume of the nucleus?

Solution:

We have,

• The radius of an atom 1A° = 10⁻¹⁰ m
• The radius of the nucleus ( Fermi ) = 10⁻¹⁵ m

Then for next steps...

Refer the attachment,

Finally, we have a volume of an atom with the volume of a nucleus.

R³_A is the radius of an atom.

R³_N is the radius of the nucleus.

Therefore, 10¹⁵ magnitudes higher is the volume of the atom as compared to the volume of the nucleus.

II.

Given:

State the number of significant figures:

(i) 0.007 m²

• It has 1 significant digit.

(ii) 2.64 × 10²⁴ kg

• It has 3 significant digit.

(iii) 0.2370 g cm⁻³

• It has 4 significant digit.

(iv) 0.2300 m

• It has 4 significant digit.

(v) 86400 m

• It has infinite significant digit.

N.B: We will not consider zeros of a number less than one as a significant digit as in first case.

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