JEE Main & CBSE Board Exams:

1. Determining Number of Protons, Neutrons, Electrons:

• Atomic number (Z) represents the number of protons in an atom.

• Mass number (A) represents the total number of protons (Z) and neutrons (N) in an atom.

$$\text{Number of neutrons (N) = Mass number (A) - Atomic number (Z)}$$

• Number of electrons (E) is equal to the number of protons (Z) for a neutral atom.

2. Average Atomic Mass:

The average atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes, taking into account their relative abundances.

Formula:

$$Average \ Atomic \ Mass = \frac{(Mass \ of \ Isotope \ 1 \times Abundance \ of \ Isotope \ 1) + (Mass \ of \ Isotope \ 2 \times Abundance \ of \ Isotope \ 2) + …}{Total \ Abundance}$$

3. Bohr’s Model Calculations:

• Radius of orbit (r) for the nth orbit:

$$r_n = \frac{n^2 h^2}{4\pi^2 m_ek Z}$$

 - \(n\) is the principal quantum number.
 - \(h\) is the Planck's constant.
 - \(k\) is the Coulomb's constant.
 - \(m_e\) is the electron mass.
 - \(Z\) is the atomic number.

• Energy of the electron in the nth orbit (E):

$$E_n = -\frac{Z e^2}{8\pi\varepsilon_0 r_n}$$

  - \(e\) is the elementary charge.
  - \(\varepsilon_0\)  is the permittivity of free space.

• Wavelength of emitted photon ((\lambda)) during transition between two orbits (n1 to n2):

$$\frac{1}{\lambda}=R_H\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$$

 - \(R_H\) is the Rydberg constant.