Physics Chapter 14: Answer key

 

Physics Answer Key

Chapter 14: Dual Nature of Radiation and Matter

---

SECTION A

Q1. Select and write the correct answer

1) The photoelectric effect supports:
The photoelectric effect supports the particle nature of light.

2) The relation E = hν was proposed by:
The relation E = hν was proposed by Max Planck.

3) Stopping potential depends on:
Stopping potential depends on the frequency of incident light.

4) Threshold frequency is:
Threshold frequency is the minimum frequency required for emission of photoelectrons.

5) Photoelectric current depends on:
Photoelectric current depends on the intensity of incident light.

6) De Broglie wavelength is given by:
De Broglie wavelength is given by the relation λ = h/mv.

7) Work function is:
Work function is the minimum energy required to emit electrons from a metal surface.

8) If frequency increases, kinetic energy of electrons:
If frequency increases, the kinetic energy of electrons increases.

9) Photoelectric effect is:
Photoelectric effect is an instantaneous process.

10) Unit of Planck’s constant is:
The unit of Planck’s constant is joule-second (J·s).

Q2. Answer in one sentence

1) Write value of speed of light (c).
The speed of light in vacuum is 3 × 10⁸ metres per second.

2) Write value of charge of electron (e).
The charge of an electron is 1.6 × 10⁻¹⁹ coulomb.

3) Write value of mass of electron (me).
The mass of an electron is 9.1 × 10⁻³¹ kilogram.

4) Write value of mass of proton (mp).
The mass of a proton is 1.67 × 10⁻²⁷ kilogram.

5) Write value of Planck’s constant (h).
Planck’s constant is 6.63 × 10⁻³⁴ joule-second.

6) Define frequency of light.
Frequency of light is defined as the number of waves passing through a given point in one second.

7) Define threshold frequency.
Threshold frequency is the minimum frequency of incident radiation required to emit photoelectrons from a metal surface.

8) Define wavelength.
Wavelength is defined as the distance between two successive crests or troughs of a wave.

9) Define work function.
Work function is the minimum amount of energy required to remove an electron from the surface of a metal.

10) Define stopping potential.
Stopping potential is the negative potential applied to stop the photoelectric current completely.

---

SECTION B (2 Marks – 4 Points)

1) What is photoelectric effect?

• Photoelectric effect is the phenomenon of emission of electrons from a metal surface when light falls on it.
• The emission occurs only when the frequency of light is above a certain minimum value.
• The emitted electrons are called photoelectrons.
• The process is instantaneous in nature.

2) State Einstein’s photoelectric equation.

• Einstein’s photoelectric equation is given by KE(max) = hν − φ.
• Here h is Planck’s constant.
• ν is the frequency of incident radiation.
• φ is the work function of the metal.

3) What is threshold wavelength?

• Threshold wavelength is the maximum wavelength of incident light that can cause emission of photoelectrons.
• If the wavelength is greater than this value, no emission occurs.
• It depends on the nature of the metal surface.
• It is related to threshold frequency by λ₀ = c/ν₀.

4) Define photoelectric current.

• Photoelectric current is the electric current produced due to the flow of photoelectrons.
• It is generated when light falls on a photosensitive surface.
• The current increases with increase in intensity of light.
• It is measured using an external circuit.

5) What is a photocell?

• A photocell is a device that converts light energy into electrical energy.
• It works on the principle of photoelectric effect.
• It consists of a photosensitive cathode and an anode.
• It produces electric current when light falls on it.

6) State applications of photocell.

• Photocells are used in exposure meters in cameras.
• They are used in burglar alarm systems.
• They are used in automatic traffic signals.
• They are used in smoke detectors.

7) What is de Broglie hypothesis?

• De Broglie hypothesis states that particles have wave nature.
• Every moving particle is associated with a wavelength.
• The wavelength is given by λ = h/p.
• It shows wave-particle duality of matter.

8) What is wave-particle duality?

• Wave-particle duality means that light and matter exhibit both wave and particle properties.
• Light behaves as a wave in interference and diffraction.
• It behaves as particles in photoelectric effect.
• This concept is fundamental in quantum physics.

9) Why does no emission occur below threshold frequency?

• Below threshold frequency, the energy of photons is insufficient.
• The energy is less than the work function.
• Therefore electrons cannot be emitted.
• Hence no photoelectric emission occurs.

10) What is stopping potential?

• Stopping potential is the negative potential applied to stop photoelectrons.
• It reduces the kinetic energy of electrons.
• At stopping potential, current becomes zero.
• It is used to measure maximum kinetic energy.

---

SECTION C (3 Marks – 6 Points)

7) Derive relation between wavelength and momentum.

• According to de Broglie hypothesis, wavelength is given by λ = h/p.
• Momentum of a particle is given by p = mv.
• Substituting the value of momentum, we get λ = h/mv.
• This shows that wavelength is inversely proportional to momentum.
• As momentum increases, wavelength decreases.
• This relation is valid for all moving particles.

8) Explain applications of photoelectric effect.

• The photoelectric effect is used in solar cells to convert sunlight into electricity.
• It is used in automatic street light systems.
• It is used in burglar alarm systems for security purposes.
• It is used in exposure meters in cameras.
• It is used in automatic doors and counters.
• It is used in smoke detectors for fire safety.

9) Why is photoelectric effect instantaneous?

• The transfer of energy from photon to electron occurs instantly.
• There is no time delay between incidence of light and emission of electrons.
• Energy is transferred in discrete packets called photons.
• Each photon interacts with one electron.
• No accumulation of energy is required.
• Hence emission takes place immediately.

---

SECTION D (Numericals)

1) Calculate energy of photon of frequency 5 × 10¹⁴ Hz.
Given: ν = 5 × 10¹⁴ Hz
Formula: E = hν
E = 6.63 × 10⁻³⁴ × 5 × 10¹⁴
E = 3.315 × 10⁻¹⁹ J

2) Find kinetic energy of electrons if frequency is 6 × 10¹⁴ Hz and work function is 2 eV.
E = hν = 3.978 × 10⁻¹⁹ J
φ = 2 eV = 3.2 × 10⁻¹⁹ J
KE = E − φ = 0.778 × 10⁻¹⁹ J

3) Calculate stopping potential if maximum kinetic energy is 3 eV.
Stopping potential V = 3 V

4) Find de Broglie wavelength of an electron accelerated through 54 V.
Formula: λ = 1.227 / √V
λ = 1.227 / √54
λ = 0.167 nm

5) Calculate wavelength of electron with kinetic energy 100 eV.
λ = 1.227 / √100
λ = 0.1227 nm

6) Calculate wavelength of electron with kinetic energy 150 eV.
λ = 1.227 / √150
λ = 0.100 nm

7) Calculate momentum of electron with wavelength 0.1 nm.
λ = 0.1 nm = 1 × 10⁻¹⁰ m
p = h / λ = 6.63 × 10⁻³⁴ / 1 × 10⁻¹⁰
p = 6.63 × 10⁻²⁴ kg·m/s

8) A student (45 kg) runs at 8 km/h. Find de Broglie wavelength.
v = 8 km/h = 2.22 m/s
p = mv = 45 × 2.22 = 100 kg·m/s
λ = h / p = 6.63 × 10⁻³⁴ / 100
λ = 6.63 × 10⁻³⁶ m

9) Find wavelength of photon of energy 3 × 10⁻¹⁹ J.
Formula: λ = hc / E
λ = (6.63 × 10⁻³⁴ × 3 × 10⁸) / 3 × 10⁻¹⁹
λ = 6.63 × 10⁻⁷ m

10) Find de Broglie wavelength of particle of mass 9.1 × 10⁻³¹ kg moving with velocity 10⁶ m/s.
p = mv = 9.1 × 10⁻³¹ × 10⁶ = 9.1 × 10⁻²⁵
λ = h / p = 6.63 × 10⁻³⁴ / 9.1 × 10⁻²⁵
λ = 7.29 × 10⁻¹⁰ m