Dual Nature of Radiation And Matter - Notes, Topics, Formulas, Books, FAQs

Important Formulas of the Dual Nature of Radiation and Matter

Important Formulas of Dual Nature of Radiation and Matter summarise the key mathematical relations that explain the particle nature of light and the wave nature of matter. These formulas are essential for analysing the photoelectric effect, understanding photon energy, and calculating the de Broglie wavelength of particles. Regular practice of these relations helps in solving numerical problems accurately in Class 12 board exams, JEE Main, and NEET.

1. Energy of a Photon:

$
E=h \nu=\frac{h c}{\lambda}
$

where
$h=$ Planck's constant,
$\nu=$ frequency,
$\lambda=$ wavelength .

2. Einstein’s Photoelectric Equation:

• Photoelectric equation

$
h \nu=\phi+K_{\max }
$

• Maximum kinetic energy of photoelectrons

$
K_{\max }=h \nu-\phi
$

3. Work Function:

$
\phi=h \nu_0
$

where $\nu_0$ is the threshold frequency.

4. Threshold Frequency:

$\nu_0=\frac{\phi}{h}$

5. Stopping Potential:

$
K_{\max }=e V_0
$

where $V_0$ is the stopping potential.

6. de Broglie Wavelength:

$\lambda=\frac{h}{p}=\frac{h}{m v}$

7. de Broglie Wavelength of an Electron (Accelerated through Potential V):

• General expression

$
\lambda=\frac{h}{\sqrt{2 m e V}}
$

• Practical form (in Å)

$
\lambda(\AA)=\frac{12.27}{\sqrt{V}}
$

8. Momentum of a Photon:

$p=\frac{h}{\lambda}$

Dual Nature of Radiation and Matter: Previous Year Questions

Past Year Questions on Dual Nature of Radiation and Matter will assist the students in knowing the kind and the frequency of questions that are commonly posed in examinations on this chapter. These questions concern primarily the photoelectric effect, the photoelectric equation by Einstein, work function, threshold frequency and de Broglie wavelength of particles. PYQs practising enhances conceptual clarity, numerical accuracy and confidence. All questions of the past years should be regularly revised, which is very useful for Class 12 board exams, JEE Main, and NEET.

Question 1:

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is ...............

Solution:

$\begin{aligned} & \mathrm{KE}_{\max }=\mathrm{h} \nu-\phi \\ & \frac{1}{2} \mathrm{mv}^2=\mathrm{h} \nu-\phi \\ & \mathrm{v}=\sqrt{\frac{2(\mathrm{~h} \nu-\phi)}{\mathrm{m}}} \\ & \text { Given } \mathrm{h} v_1=2 \phi \\ & \mathrm{~h} v_2=10 \phi \\ & \therefore \frac{\mathrm{v}_1}{\mathrm{v}_2}=\sqrt{\frac{\mathrm{h} v_1-\phi}{\mathrm{h} v_2-\phi}} \\ & \frac{\mathrm{v}_1}{\mathrm{v}_2}=\sqrt{\frac{2 \phi-\phi}{10 \phi-\phi}}=\frac{1}{3}\end{aligned}$

Question 2:

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm , the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to

Solution:

$\begin{aligned} & \mathrm{K}_1=\mathrm{hc} / \lambda_1-\Phi_0 \\ & \mathrm{~K}_2=\mathrm{hc} / \lambda_2-\Phi_0 \\ & \therefore \mathrm{~K}_2=3 \mathrm{~K}_1 \\ & \Rightarrow 3\left[\mathrm{hc} / 500-\Phi_0\right] \\ & =\mathrm{hc} / 200-\Phi_0 \\ & \Rightarrow \Phi_{0}=0.61 \mathrm{eV}\end{aligned}$

Question 3:

The surface of a metal is illuminated alternately with photons of energies $E_1=4 \mathrm{eV}$ and $E_2=2.5 \mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2 . The work function of the metal in $(\mathrm{eV})$ is

Solution:

$
\begin{aligned}
& E_1=\phi+K_1 \ldots(1) \\
& E_2=\phi+K_2 \ldots(2) \\
& E_1-E_2=K_1-K_2 \\
& \text { Now } \frac{V_1}{V_2}=2 \\
& \frac{K_1}{K_2}=4 \\
& K_1=4 K_2
\end{aligned}
$
Now from equation (2)

$
\begin{aligned}
& \Rightarrow 4-2.5=4 K_2-K_2 \\
& 1.5=3 K_2 \\
& K_2=0.5 \mathrm{eV}
\end{aligned}
$
Now putting This
Value in equation (2)

$
\begin{aligned}
& 2.5=\phi+0.5 \mathrm{eV} \\
& \phi=2 \mathrm{eV}
\end{aligned}
$

Dual Nature of Radiation and Matter in Different Exams

Chapter Dual Nature of Radiation and Matter is one of the most important chapters in Class 12 Physics that offers students a new introduction to the basics of quantum physics. This chapter questions the concept of photoelectric effect, wave-particle duality, and the de Broglie wavelength, and are largely conceptual with easy number values. Being aware of the focus and weightage of exams helps students to be effective and score high in the various examinations.

Important Books and Resources for Class 12: Dual Nature of Radiation and Matter

Students need to use the NCERT textbook, model problems with the chapter Dual Nature of Radiation and Matter, and strong reference books that teach how to understand the photoelectric effect, wave-particle duality, de Broglie hypothesis, and other related experiments with clarity and examples to master the chapter. These books assist in developing a good conceptual knowledge and problem-solving abilities, which are required not only in Class 12 board examinations, but also in competitive examinations such as JEE Main, JEE Advanced and NEET.

NCERT Resources for Dual Nature of Radiation and Matter

The most significant study materials in acquiring the basic concepts of wave-particle duality as required in the Class 12 Physics syllabus are the NCERT materials in Dual Nature of Radiation and Matter. The NCERT textbook and exemplar problems clearly explain concepts such as the photoelectric effect, Einstein's photoelectric equation, work function, and de Broglie wavelength using standard definitions, graphs, and examples. Good preparation using the NCERT material is the key to a good score in Class 12 board exams, NEET, and JEE Main because the majority of questions in this chapter are directly NCERT-based.

• NCERT solutions for Class 12 Physics Chapter 11 Dual nature of radiation and matter
• NCERT Exemplar Class 12 Physics Solutions Chapter 11
• NCERT notes Class 12 Physics Chapter 11 Dual nature of radiation and matter

NCERT Subjectwise Resources

NCERT subject-wise materials are organised and syllabus-based learning content on various subjects, which assists students in developing a good conceptual basis. They consist of textbooks, exemplar problems, and solutions and can thus be very helpful in the preparation for the board exams and even competitive exams such as JEE and NEET.

Practice Questions based on the Dual Nature of Radiation and Matter

Dual Nature of Radiation and Matter Practice Questions are used to reinforce the ordering of knowledge students have about the quantum phenomenon of light and matter. These questions concern primarily the photoelectric effect, the photoelectric equation by Einstein, work function, threshold frequency and de Broglie wavelength of particles. Regular practice improves conceptual clarity, numerical accuracy, and confidence in applying formulas. Solving a range of problems is very useful both to Class 12 board examination and competitive examinations such as JEE Main and NEET.

Conclusion

In the chapter Dual Nature of Radiation and Matter, a very solid background on how light and material particles behave on a quantum level is established. Developing clear and accurate conceptual knowledge in students can be achieved by revising basic notions, key formulas, and experimental descriptions of the photoelectric effect, the concept of wave-particle duality, and the de Broglie hypothesis. This focused preparation enhances confidence and proves highly effective for performing well in Class 12 board examinations as well as competitive exams like JEE Main and NEET.