DC Pandey Modern Physics-1 Solutions

DC Pandey Optics and Modern Physics Solutions for Chapter 29 ‘Modern Physics 1’ will assist you in understanding the concepts of this chapter for JEE Physics and Class 12 board exams. In ‘Modern Physics-1’ of DC Pandey Physics Book Solutions, you will be introduced to the dual nature of the electromagnetic waves, electromagnetic spectrum, momentum, radiation pressure and the de-Broglie wavelength of matter-wave. You will also get to explore early atomic structures, the Bohr hydrogen atom, reduced mass, X-rays, emission of electrons and the photoelectric effect.

DC Pandey Modern Physics 1 consists of 136 questions. These questions are covered in a total of 3 exercises arranged in the order of increasing difficulty. By solving these questions, you will be able to brush up the concepts of ionization energy, the mass of electrons, the energy of photons, intensity of light, rate of change of momentum of photons and the photoelectric effect. It is advised that you solve all the exercises consistently to prepare well for your Class 12 CBSE Board Exams. 

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Important Topics in DC Optics and Modern Physics Solutions Chapter 29: Modern Physics 1

Dual Nature of Electromagnetic Waves

We regard electromagnetic waves since they undergo the phenomena of diffraction, polarisation, and interference. This was demonstrated by Young’s double-slit experiment which we covered in the previous chapter. 

Also, in different situations, the light waves (which lie in the band of wavelengths of electromagnetic waves) behave like a string of particles. Such properties of wave and particle exhibited at once by the electromagnetic waves suggest that they have dual nature.

According to Einstein, the energy of a particle of light called a photon is given as,

, where h is Planck’s constant and c is the speed of light.

Electromagnetic spectrum

The electromagnetic spectrum is the classification of waves on the basis of their frequencies. These waves are:

  1. Radio waves with a frequency range of 500-1000 MHz
  2. Microwaves
  3. Infrared rays
  4. Visible rays with a wavelength of 700-400 nm.
  5. Ultraviolet rays
  6. X-rays
  7. Gamma rays

Momentum and Radiation Pressure

The momentum, p is given by: 

p=E/q where E is the energy discussed in the sections above and c stands for the speed of light.

Radiation pressure is equivalent to the energy density, u.

For a totally absorbed wave of intensity I,

For a totally reflected wave,

de-Broglie Wavelength of Matter Wave

According to de-Broglie, the wavelength for a photon moving with frequency f and a wavelength λ has energy,

He suggested that a mass m moving with momentum p and a velocity v exhibits wave nature with a wavelength λ=h/p

Because for Kinetic Energy of the photon K and K=qV for a charge q accelerated by a potential difference V, the de-Broglie wavelength, 

Early Atomic Structures

Early Atomics Structures include the models given by JJ Thomson, Rutherford, and many more. JJ Thomson suggested that the atoms are like a plum pudding which is positively charged and the electrons are embedded in it like raisins.

Rutherford suggested that all the positive charge is concentrated in the centre of an atom and the negatively charged electrons revolve around the positive charge like the planets revolve around the sun. He suggested a centripetal force due to the force of attraction between opposite charges can hold the movement together.

Bohr Hydrogen Atom

Bohr suggested that there was specific energy that each circular orbit of an electron exhibited and an electron radiated energy only when it shifted to another orbit. The energy is radiated as a photon and has the energy and frequency given as,

For a mass m moving with velocity v in a circular motion of radius r, momentum L= mvr and Bohr suggested angular momentum

Therefore, , where n is the principal quantum number.

For nth orbit, radius , and velocity,  and energy level

Reduced Mass

It can be given as,

Where gives the reduced mass, m is the mass of the replaced electron and M is the mass of the nucleus of the atom.


X-rays can be produced using a Coolidge tube and of two types- continuous and characteristic depending upon the accelerating potential difference or the target respectively.

Exercise Discussion for DC Pandey Optics and Modern Physics Solutions Chapter 29: Modern Physics 1

  • The chapter includes 2 introductory exercises with around 25 questions. Introductory Exercise 29.1 comprises questions in which you will need in-depth knowledge of concepts of the electromagnetic spectrum, momentum, radiation pressure, the de-Broglie wavelength of matter-wave.
  • In Exercise 29.2 you will get to solve questions about reduced mass and evaluation of maximum kinetic energy. 
  • Then, there are two sets of exercises comprises of 2 levels of subjective questions and multiple-choice questions. The topics covered in the questions of each section include the Bohr atomic model and emission spectrum, and the photoelectric effect.
  • At last, there is an exercise called JEE Corner where you will get to solve more advanced level questions of the topics of the chapter. This includes matching the columns questions Balmer Series, assertion and reason questions and other objective questions. 

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