NEET Dual Nature of Matter — Set 2

Question 1

A $ 30 \, \text{kV} $ X-ray tube produces X-rays. What is the minimum wavelength of the emitted X-rays? (Take $ h = 6.63 \times 10^{-34} \, \text{J s} $, $ c = 3 \times 10^8 \, \text{m/s} $, $ e = 1.6 \times 10^{-19} \, \text{C} $)

Accepted Answer

Energy $ E = e V = 1.6 \times 10^{-19} \times 30 \times 10^3 = 4.8 \times 10^{-15} \, \text{J} $. $ \lambda_{\min} = \frac{h c}{E} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{4.8 \times 10^{-15}} \approx 4.14 \times 10^{-11} \, \text{m} = 0.0414 \, \text{nm} $.

Question 2

The work function of a metal is $ 3.0 \, \text{eV} $. Light of frequency $ 8.0 \times 10^{14} \, \text{Hz} $ is incident on it. What is the stopping potential? (Take $ h = 6.63 \times 10^{-34} \, \text{J s} $, $ e = 1.6 \times 10^{-19} \, \text{C} $)

Accepted Answer

$ E = h v = 6.63 \times 10^{-34} \times 8.0 \times 10^{14} = 5.304 \times 10^{-19} \, \text{J} $. $ E = \frac{5.304 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 3.315 \, \text{eV} $. $ K_{\max} = E - \phi_0 = 3.315 - 3.0 = 0.315 \, \text{eV} $. $ V_0 = \frac{K_{\max}}{e} = 0.315 \, \text{V} $.

Question 3

An electron is accelerated through $ 50 \, \text{V} $. What is its de Broglie wavelength? (Take $ h = 6.63 \times 10^{-34} \, \text{J s} $, $ m_e = 9.11 \times 10^{-31} \, \text{kg} $, $ e = 1.6 \times 10^{-19} \, \text{C} $)

Accepted Answer

$ K = e V = 1.6 \times 10^{-19} \times 50 = 8.0 \times 10^{-18} \, \text{J} $. $ p = \sqrt{2 m K} = \sqrt{2 \times 9.11 \times 10^{-31} \times 8.0 \times 10^{-18}} \approx 3.816 \times 10^{-24} \, \text{kg m/s} $. $ \lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34}}{3.816 \times 10^{-24}} \approx 1.737 \times 10^{-10} \, \text{m} = 0.1737 \, \text{nm} $.

NEET Physics: Dual Nature of Matter — Practice Set 2

Q1. A \( 30 \, \text{kV} \) X-ray tube produces X-rays. What is the minimum wavelength of the emitted X-rays? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

Q2. The work function of a metal is \( 3.0 \, \text{eV} \). Light of frequency \( 8.0 \times 10^{14} \, \text{Hz} \) is incident on it. What is the stopping potential? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

Q3. An electron is accelerated through \( 50 \, \text{V} \). What is its de Broglie wavelength? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( m_e = 9.11 \times 10^{-31} \, \text{kg} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

Q4. The maximum kinetic energy of photoelectrons is \( 0.5 \, \text{eV} \) when light of frequency \( 6.0 \times 10^{14} \, \text{Hz} \) is used. What is the threshold frequency? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

Q5. The de Broglie wavelength of a particle of mass \( 3.0 \times 10^{-30} \, \text{kg} \) moving at \( 1.0 \times 10^6 \, \text{m/s} \) is:

Q6. Light of wavelength \( 300 \, \text{nm} \) produces a stopping potential of \( 1.5 \, \text{V} \). What is the work function of the metal in eV? (Take \( h c = 1240 \, \text{eV nm} \))

Q7. The work function of a metal is \( 1.8 \, \text{eV} \). What is the threshold frequency for this metal? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

Q8. In the context of matter waves, what property of a moving particle is inversely proportional to its de Broglie wavelength?

Q9. A light source emits \( 1.0 \times 10^{16} \) photons per second with a power of \( 4.0 \, \text{mW} \). What is the wavelength of the light? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \))

Q10. Which of the following is a characteristic of the photoelectric effect that the classical wave theory fails to explain?