Structure of Atom: Comprehensive NEET Chemistry Formulae Summary

1. Key Formulae and Explanations

1.1 Charge to Mass Ratio of Electron

The charge to mass ratio of an electron was determined by J.J. Thomson through cathode ray experiments.

$\frac{e}{m_e}=1.758820\times 10^{11}\text{C}{\text{kg}}^{-1}$

• Explanation: This ratio signifies the amount of charge per unit mass for an electron. It is crucial in understanding the behavior of electrons in electric and magnetic fields.

1.2 Charge on the Electron

The charge on a single electron was measured by R.A. Millikan using the oil drop experiment.

$e=-1.602176\times 10^{-19}\text{C}$

• Explanation: This value represents the elementary charge, the smallest charge found in nature, carried by a single electron. It is a fundamental constant in physics.

1.3 Mass of the Electron

By combining the charge to mass ratio and the charge on the electron, the mass of the electron can be calculated.

$m_e=9.1094\times 10^{-31},\text{kg}$

• Explanation: This mass is extremely small, reflecting the tiny size and mass of an electron compared to protons and neutrons.

1.4 Atomic Number (Z) and Mass Number (A)

The atomic number and mass number are fundamental quantities used to describe atoms.

• Atomic Number: $Z=\text{Number of protons in the nucleus}$
• Mass Number: $A=\text{Number of protons}+\text{Number of neutrons}$
• Explanation: The atomic number defines the element, while the mass number gives the total count of protons and neutrons in an atom's nucleus.

1.5 Relationship between Frequency, Wavelength, and Speed of Light

The relationship between these quantities for electromagnetic radiation is given by:

$c=\nu \lambda$

Where:

• $c$ is the speed of light in a vacuum ($3\times 10^8\text{m/s}$),
• $\nu$ is the frequency of the radiation,
• $\lambda$ is the wavelength of the radiation.
• Explanation: This fundamental equation is used in various contexts to relate the frequency and wavelength of light and other electromagnetic waves.

1.6 Planck's Quantum Theory

The energy of a quantum of radiation is given by:

$E=h\nu$

Where:

• $E$ is the energy,
• $h$ is Planck's constant ($6.626\times 10^{-34}\text{J s}$),
• $\nu$ is the frequency of the radiation.
• Explanation: This equation forms the basis of quantum mechanics, showing that energy is quantized and can be absorbed or emitted in discrete amounts.

1.7 Bohr’s Model for Hydrogen Atom

The energy of an electron in a hydrogen atom is quantized and given by:

$E_n=-\frac{R_H}{n^2}$

Where:

• $R_H$ is the Rydberg constant for hydrogen ($2.18\times 10^{-18}\text{J}$),
• $n$ is the principal quantum number.
• Explanation: This equation describes the energy levels of electrons in a hydrogen atom. Electrons can only occupy certain energy levels, leading to the discrete lines observed in the hydrogen spectrum.

2. Common Mistakes in Applying These Formulae

2.1 Incorrect Unit Conversion

A common error is converting units incorrectly, particularly when dealing with energy (Joules vs. electron volts) or wavelength (meters vs. nanometers).

NEET Tip:

Always ensure unit consistency when applying formulas, particularly in calculations involving energy and wavelength.

2.2 Misinterpretation of Quantum Numbers

Students often confuse the principal quantum number with other quantum numbers, leading to incorrect energy level calculations.

Mnemonic:

Remember, "n" stands for "number" and represents the principal quantum number, which dictates the energy level in the Bohr model.

3. Example Problems

Problem 1: Calculation of Electron's Energy Level

Question: Calculate the energy of an electron in the second orbit (n = 2) of a hydrogen atom.

Solution: Using Bohr’s energy formula:

$E_2=-\frac{2.18\times 10^{-18}\text{J}}{2^2}=-0.545\times 10^{-18}\text{J}$

Problem 2: Wavelength of Emitted Photon

Question: Calculate the wavelength of light emitted when an electron transitions from n=3 to n=2 in a hydrogen atom.

Solution: First, find the energy difference:

$\Delta E=E_3-E_2=-\frac{2.18\times 10^{-18}}{3^2}-\left(-\frac{2.18\times 10^{-18}}{2^2}\right)$

$\Delta E=-2.42\times 10^{-19}\text{J}$

Now, use the relation:

$\lambda =\frac{hc}{\Delta E}$

4. Quick Recap

• Charge to mass ratio of electron: $\frac{e}{m_e}=1.758820\times 10^{11}\text{C}{\text{kg}}^{-1}$
• Energy of a quantum of radiation: $E=h\nu$
• Bohr's energy levels: $E_n=-\frac{R_H}{n^2}$
• Wavelength-frequency relation: $c=\nu \lambda$

5. Concept Connection

Link to Physics: Quantum Mechanics

The principles of energy quantization in atomic physics directly connect with quantum mechanics in physics, particularly when dealing with wave-particle duality and the behavior of subatomic particles.

Link to Biology: Photosynthesis

Understanding the interaction of light with matter, such as the absorption of photons, is crucial in biological processes like photosynthesis, where light energy is converted into chemical energy.

This summary captures the essential formulae and concepts from the "Structure of Atom" chapter, with explanations, common errors, and example problems tailored for NEET preparation.