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?
Radius of atom = 1Å = 10-10 m
Radius of nucleus = 1 fermi = 10-15 m
Volume of atom = Va = $\frac{4}{3}\pi R_{A}^{3}$
Volume of nucleus Vn = $\frac{4}{3}\pi R_{N}^{3}$
$\frac{V_{a}}{V_{n}}=\frac{\frac{4}{3}\pi R_{A}^{3}}{\frac{4}{3}\pi R_{N}^{3}}=\left(\frac{R_{A}}{R_{N}}\right)^{3} = \left(\frac{10^{-10}}{10^{-15}}\right)^{3} = 10^{15}$
Note: In such type of questions, always change the value in the same unit.
Name the device used for measuring the mass of atoms and molecules.
The device used for measuring the mass of atoms and molecules is called a mass spectrometer. Mass spectrometry involves ionizing chemical compounds to generate charged molecules or molecule fragments and measuring their mass-to-charge ratios.
Express unified atomic mass unit in kg.
One atomic mass unit is the $\frac{1}{12}$ of the mass of a 6 12C atom.
Mass of one mole of 612 C12 atom = 12 g
Number of atoms in one mole = Avogadro's number = 6.023 × 1023
A function $f(\theta)$ is defined as $f(\theta) = 1 - \theta + \frac{\theta^2}{2!} - \frac{\theta^3}{3!} + \frac{\theta^4}{4!} + \ldots$
Why is it necessary for $f(\theta)$ to be a dimensionless quantity?
Since $f(\theta)$ is a sum of different powers of $\theta$ and it is a dimensionless quantity. By principle of homogeneity as RHS is dimensionless, hence LHS should also be dimensionless.
Why length, mass and time are chosen as base quantities in mechanics?
Length, mass and time are chosen as base quantities in mechanics because:
(i) Length, mass and time cannot be derived from one another, that is these quantities are independent.
(ii) All other quantities in mechanics can be expressed in terms of length, mass and time.