Question 1
Find (a) the maximum frequency and (b) the minimum wavelength of X-rays produced by electrons accelerated through 30 kV.
Steps only
E_max=30 keV=eV; ν_max=E/h=7.25×10¹⁸ Hz and λ_min=hc/E=4.13×10⁻¹¹ m.
Answer
7.25×10¹⁸ Hz; 0.0413 nm.
CLASS 12 · PHYSICS · CHAPTER 11
Dual Nature of Radiation and Matter
Clear, worked answers to all eleven end-of-chapter exercises on photons, photoelectric emission, and matter waves.
11 worked answersComplete chapter answers
11 worked answers · short steps first, explanations when you need them
Chapter 11 Exercises
Textbook pages Chapter exercise section
Question 2
Caesium has work function 2.14 eV. Light of frequency 6×10¹⁴ Hz falls on it. Find (a) the maximum kinetic energy of emitted electrons, (b) the stopping potential, and (c) their maximum speed.
Steps only
hν=2.48 eV; K_max=2.48−2.14=0.34 eV, so V₀=0.34 V. v=√(2K/mₑ)≈3.46×10⁵ m/s.
Answer
0.34 eV; 0.34 V; 3.46×10⁵ m/s.
Question 3
In a photoelectric experiment, the cut-off voltage is 1.5 V. What is the maximum kinetic energy of the emitted photoelectrons?
Steps only
K_max=eV₀=1.5 eV=2.40×10⁻¹⁹ J.
Answer
1.5 eV (2.40×10⁻¹⁹ J).
Question 4
A helium-neon laser emits 632.8 nm light with power 9.42 mW. Find (a) the energy and momentum of each photon, (b) the average number of photons arriving at a target each second, and (c) the speed a hydrogen atom needs to have the same momentum as one photon.
Steps only
E=hc/λ=3.14×10⁻¹⁹ J; p=h/λ=1.05×10⁻²⁷ kg m/s; N=P/E=3.00×10¹⁶ s⁻¹; v_H=p/m_H≈0.63 m/s.
Answer
3.14×10⁻¹⁹ J; 1.05×10⁻²⁷ kg m/s; 3.00×10¹⁶ photons/s; 0.63 m/s.
Question 5
The slope of the cut-off-voltage versus incident-frequency graph is 4.12×10⁻¹⁵ V s. Calculate Planck's constant.
Steps only
Slope=h/e, so h=e×slope=(1.602×10⁻¹⁹)(4.12×10⁻¹⁵)=6.60×10⁻³⁴ J s.
Answer
6.60×10⁻³⁴ J s.
Question 6
A metal has threshold frequency 3.3×10¹⁴ Hz. Light of frequency 8.2×10¹⁴ Hz shines on it. Predict the cut-off voltage.
Steps only
V₀=(h/e)(ν−ν₀)=4.136×10⁻¹⁵×4.9×10¹⁴≈2.03 V.
Answer
About 2.0 V.
Question 7
A metal has work function 4.2 eV. Will light of wavelength 330 nm cause photoelectric emission?
Steps only
E=hc/λ≈1240/330=3.76 eV<4.2 eV.
Answer
No photoelectric emission.
Question 8
Light of frequency 7.21×10¹⁴ Hz ejects electrons with maximum speed 6.0×10⁵ m/s. Find the metal's threshold frequency.
Steps only
K=½mₑv²=1.64×10⁻¹⁹ J; ν₀=ν−K/h=7.21×10¹⁴−2.47×10¹⁴=4.74×10¹⁴ Hz.
Answer
4.74×10¹⁴ Hz.
Question 9
An argon laser produces light of wavelength 488 nm. When it shines on a photoelectric emitter, the stopping potential is 0.38 V. Find the emitter's work function.
Steps only
φ=hc/λ−eV₀≈1240/488−0.38=2.16 eV.
Answer
2.16 eV.
Question 10
Find the de Broglie wavelength of (a) a 0.040 kg bullet moving at 1.0 km/s, (b) a 0.060 kg ball moving at 1.0 m/s, and (c) a 1.0×10⁻⁹ kg dust particle drifting at 2.2 m/s.
Steps only
λ=h/(mv): (a) 1.66×10⁻³⁵ m; (b) 1.10×10⁻³² m; (c) 3.01×10⁻²⁵ m.
Answer
(a) 1.66×10⁻³⁵ m; (b) 1.10×10⁻³² m; (c) 3.01×10⁻²⁵ m.
Question 11
Show that the wavelength of electromagnetic radiation equals the de Broglie wavelength of its photon.
Steps only
p=E/c=hν/c=h/λ. Hence λ_dB=h/p=λ.
Answer
The photon’s de Broglie wavelength is the same as its radiation wavelength.