Find the best tutors and institutes for Class 12 Tuition
Q11.2(c):
The work function of caesium metal is 2.14 eV. When light of frequency (6 \times 10^{14})Hz is incident on the metal surface, photoemission of electrons occurs. What is the maximum speed of the emitted photoelectrons?
Solution :
Step 1: Given Variables & Initial Setup
To determine the maximum speed ($v_{max}$) of the emitted photoelectrons, we utilize the Photoelectric Equation formulated by Albert Einstein. [Per the Law of Conservation of Energy in photoelectric emission].
- Work function of Caesium ($\Phi_0$): $2.14\text{ eV}$
- Frequency of incident light ($\nu$): $6 \times 10^{14}\text{ Hz}$
- Planck’s constant ($h$): $6.626 \times 10^{-34}\text{ J}\cdot\text{s}$
- Mass of an electron ($m_e$): $9.11 \times 10^{-31}\text{ kg}$
- Conversion factor ($1\text{ eV} = 1.6 \times 10^{-19}\text{ J}$)
Step 2: Conversion of Work Function to Joules
For consistency in SI units, we convert $\Phi_0$ from electron-volts to Joules:
$\Phi_0 = 2.14 \times 1.6 \times 10^{-19}\text{ J} = 3.424 \times 10^{-19}\text{ J}$
Step 3: Calculating Energy of Incident Photons ($E$)
Using the photon energy formula $E = h\nu$:
$E = (6.626 \times 10^{-34}\text{ J}\cdot\text{s}) \times (6 \times 10^{14}\text{ Hz})$
$E = 3.9756 \times 10^{-19}\text{ J}$
Step 4: Calculating Maximum Kinetic Energy ($K_{max}$ )
Applying the photoelectric equation: $K_{max} = E - \Phi_0$ [Per Einstein's Photoelectric Equation].
$K_{max} = 3.9756 \times 10^{-19}\text{ J} - 3.424 \times 10^{-19}\text{ J}$
$K_{max} = 0.5516 \times 10^{-19}\text{ J} = 5.516 \times 10^{-20}\text{ J}$
Step 5: Determining Maximum Speed ($v_{max}$)
Since $K_{max} = \frac{1}{2}m_e v_{max}^2$, we isolate $v_{max}$:
$v_{max} = \sqrt{\frac{2K_{max}}{m_e}}$
$v_{max} = \sqrt{\frac{2 \times 5.516 \times 10^{-20}}{9.11 \times 10^{-31}}}$
$v_{max} = \sqrt{1.211 \times 10^{11}}$
$v_{max} \approx 3.48 \times 10^{5}\text{ m/s}$
Visual Representation of Photoelectric Emission
Final Solution: The maximum speed of the emitted photoelectrons is approximately $3.48 \times 10^5\text{ m/s}$.
More Questions from Class 12 Physics Dual Nature of Radiation and Matter EXERCISES
- Q11.1(a): Find the (a) maximum frequency of X-rays produced by $30$ kV electrons.
- Q11.1(a): Find the maximum frequency of X-rays produced by 30 kV electrons.
- Q11.1(b): Find the minimum wavelength of X-rays produced by 30 kV electrons.
- Q11.1(b): Find the (b) minimum wavelength of X-rays produced by $30$ kV electrons.
- Q11.10(a): What is the de Broglie wavelength of a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s?
- Q11.10(a): What is the de Broglie wavelength of (a) a bullet of mass $0.040$ kg travelling at the speed of $1.0$ km/s,
- Q11.10(b): What is the de Broglie wavelength of a ball of mass 0.060 kg moving at a speed of 1.0 m/s?
- Q11.10(b): What is the de Broglie wavelength of (b) a ball of mass $0.060$ kg moving at a speed of $1.0$ m/s, and
- Q11.10(c): What is the de Broglie wavelength of a dust particle of mass (1.0 \times 10^{-9}) kg drifting with a speed of 2.2 m/s ?
- Q11.10(c): What is the de Broglie wavelength of (c) a dust particle of mass $1.0 \times 10^{-9}$ kg drifting with a speed of $2.2$ m/s ?
- Q11.11: Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
- Q11.11: Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
- Q11.2(a): The work function of caesium metal is 2.14 eV. When light of frequency (6 \times 10^{14})Hz is incident on the metal surface, photoemission of electrons occurs. What is the maximum kinetic energy of the emitted electrons?
- Q11.2(a): The work function of caesium metal is $2.14$ eV. When light of frequency $6 \times 10^{14}$Hz is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons,
- Q11.2(b): The work function of caesium metal is 2.14 eV. When light of frequency (6 \times 10^{14})Hz is incident on the metal surface, photoemission of electrons occurs. What is the Stopping potential?
- Q11.2(b): The work function of caesium metal is $2.14$ eV. When light of frequency $6 \times 10^{14}$Hz is incident on the metal surface, photoemission of electrons occurs. What is the (b) Stopping potential, and
- Q11.2(c): The work function of caesium metal is $2.14$ eV. When light of frequency $6 \times 10^{14}$Hz is incident on the metal surface, photoemission of electrons occurs. What is the (c) maximum speed of the emitted photoelectrons?
- Q11.3: The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?
- Q11.3: The photoelectric cut-off voltage in a certain experiment is $1.5$ V. What is the maximum kinetic energy of photoelectrons emitted?
- Q11.4(a): Monochromatic light of wavelength $632.8$ nm is produced by a helium-neon laser. The power emitted is $9.42$ mW. (a) Find the energy and momentum of each photon in the light beam,
- Q11.4(a): Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. Find the energy and momentum of each photon in the light beam,
- Q11.4(b): Monochromatic light of wavelength $632.8$ nm is produced by a helium-neon laser. The power emitted is $9.42$ mW. (b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and
- Q11.4(b): Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area ), and
- Q11.4(c): Monochromatic light of wavelength $632.8$ nm is produced by a helium-neon laser. The power emitted is $9.42$ mW. (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
- Q11.4(c): Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
- Q11.5: In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be $4.12 \times 10^{-15}$ V s. Calculate the value of Planck’s constant.
- Q11.5: In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be (4.12 \times 10^{-15}) V s. Calculate the value of Planck’s constant.
- Q11.6: The threshold frequency for a certain metal is $3.3 \times 10^{14}$ Hz. If light of frequency $8.2 \times 10^{14}$ Hz is incident on the metal, predict the cut-off voltage for the photoelectric emission.
- Q11.6: The threshold frequency for a certain metal is (3.3 \times 10^{14}) Hz. If light of frequency (8.2 \times 10^{14}) Hz is incident on the metal, predict the cut-off voltage for the photoelectric emission.
- Q11.7: The work function for a certain metal is $4.2$ eV. Will this metal give hotoelectric emission for incident radiation of wavelength $330$ nm?
- Q11.7: The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
- Q11.8: Light of frequency $7.21 \times 10^{14}$ Hz is incident on a metal surface. Electrons with a maximum speed of $6.0 \times 10^{5}$ m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
- Q11.8: Light of frequency (7.21 \times 10^{14}) Hz is incident on a metal surface. Electrons with a maximum speed of (6.0 \times 10^{5}) m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
- Q11.9: Light of wavelength $488$ nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-of f) potential of photoelectrons is $0.38$ V. Find the work function of the material from which the emitter is made.
- Q11.9: Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.
CBSE Solutions for Class 12 Physics Dual Nature of Radiation and Matter
Chapters in CBSE - Class 12 Physics
- Electric Charges and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Waves
- Ray Optics and Optical Instruments
- Wave Optics
- Atoms
- Nuclei
- Semiconductor Electronics
- Communication Systems
Top Tutors who teach Dual Nature of Radiation and Matter
Top Tutor
Krishnarajapura, Bangalore
10 yrs of
Exp
5 students
339 hrs of classes completed
500
per hour
Online Classes
Tutor's home
I am an IITian. Passed out from IIT Delhi. Teaching is my passion. I have seven years of teaching experience teach chemistry, Biology ,Biochemistry, Biotechnology for class 11 and 12 from different boards.I teach chemistry for entrance exams like NEET, JEE.
Anasuya mam teaches each topic in detail and giving excellent support in JEE chemistry preparations.
Top Tutor
CUC, Gachibowli, Hyderabad
5 yrs of
Exp
2 students
3 hrs of classes completed
375
per hour
Online Classes
I am avid learner of Science and have helped several students improve their understanding and hence academic performances.Currently,I am doing my Ph.d. in Mathematics from IISER Bhopal. I have done my Bachelors in Mathematics from IGNOU. I have also completed M.Sc. in Pure Mathematics from University of Hyderabad in 2024. I have successfully managed to clear GATE, NET JRF in Mathematical science..To spread my love for Mathematics and Physics I have been teaching Mathematics and Physics for the past 6 years (std 9-12, B.Sc and M.Sc). So ,If you want to understand the concepts of mathematics and physics, I am here to help you with that. I also provide Customized notes and exercise to focus on the area of improvement .Classes are recorded so that you can go through them anytime and refresh/ revise the topics. I have all the necessary tools for online classes. So, hope to see you in Demo.
It was a very nice experience. He went very in-depth and clear. It was very useful. I studied maths for CBSE board.
Super Tutor
Sector 59 E Block, Noida
6 yrs of
Exp
104 students
1774 hrs of classes completed
300
per hour
Online Classes
In my role as a teacher for Class 12, I've had the privilege of fostering a dynamic and engaging learning environment. Utilizing a combination of traditional teaching methods and modern technology, I've been able to ensure that students remain both interested and challenged. I've consistently strived to create a classroom atmosphere that promotes curiosity and encourages students to ask questions, facilitating a deeper understanding of the subject matter. As a Class 12th mentor, my goal has been to equip students not only with academic knowledge but also with the skills necessary for their future endeavors.
Very good teacher, the explanation was nice, i was able to understand all the little concepts that too in a short span of time.
Super Tutor
Lalpur, Ranchi
9 yrs of
Exp
8 students
2973 hrs of classes completed
600
per hour
Online Classes
I am a qualified and dedicated teacher, having 10 years of teaching and research experience across different boards including CBSE, ICSE, IGCSE, IB, GCSE, and Australian Board. I specialize in guiding students from Class 8 to Post Graduation, helping them achieve academic excellence with a tailored and engaging teaching approach. I bring in-depth knowledge and expertise to my sessions. Qualifications: • Ph. D (Science) – BIT Mesra, Ranchi • CSIR UGC NET (2011) AIR-14 • ICAR NET (2010) • ICAR NET (2018) • GATE (2009) My student-centered approach focuses on assessing individual learning needs, bridging knowledge gaps, and fostering critical thinking through interactive methods like discussions, visual aids, and hands-on activities. Regular feedback and personalized guidance empower students to excel and develop a lifelong love for learning.
Top Tutor
Choolissery, Thrissur
20 yrs of
Exp
1 student
396 hrs of classes completed
600
per hour
Online Classes
I'm Sini Jayaraj, and I'm excited to hear about your interest in Class 12 tuition. With over 20 years of experience teaching subjects like Mathematics, Physics, Chemistry, and Science, Teaching is my passion.... Enjoyed well in highschool and higher secondary level.. l'm confident I can help you excel, especially given your immediate start timeline.My background includes a B.Sc., B.Ed., and M.Sc., allowing me to provide a comprehensive understanding of the subjects. I have taught for 214 hours.I focus on making complex topics easy to grasp, perfectly aligning with your goal of simplifying the learning process.Would you be interested in booking a free demo class with me to discuss your specific needs and how I can support you? Or feel free to connect with me to discuss further.Warm regards,Sini Jayaraj secondary levels
Sini mam is very responsible and sinsere teaches. She knows how to teach kids actively &make undestand them concepts clearly.
Other Subjects in CBSE - Class 12
Download free CBSE - Class 12 Physics Dual Nature of Radiation and Matter EXERCISES worksheets
Download Now
