Dual Nature of Matter Chapter-Wise Test 8

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What happens to photoelectric emission if the frequency of incident light is below the threshold frequency?

No photoelectric emission occurs if the frequency is below the threshold frequency, as the photon energy (\( h v \)) is less than the work function (\( \phi_0 \)).

Increases
Decreases
Remains constant
Stops completely
4

The de Broglie wavelength of a particle of mass \( 5.0 \times 10^{-30} \, \text{kg} \) moving at \( 2.0 \times 10^5 \, \text{m/s} \) is:

Momentum \( p = m v = 5.0 \times 10^{-30} \times 2.0 \times 10^5 = 1.0 \times 10^{-24} \, \text{kg m/s} \).

\( \lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34}}{1.0 \times 10^{-24}} = 6.63 \times 10^{-10} \, \text{m} = 0.663 \, \text{nm} \).

0.6 nm
0.663 nm
0.7 nm
0.8 nm
2

The threshold frequency of a metal is \( 4.8 \times 10^{14} \, \text{Hz} \). What is the maximum kinetic energy for light of frequency \( 6.8 \times 10^{14} \, \text{Hz} \)? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

\( \phi_0 = h v_0 = 6.63 \times 10^{-34} \times 4.8 \times 10^{14} = 3.1824 \times 10^{-19} \, \text{J} \).

\( E = h v = 6.63 \times 10^{-34} \times 6.8 \times 10^{14} = 4.5084 \times 10^{-19} \, \text{J} \).

\( K_{\max} = E - \phi_0 = 4.5084 \times 10^{-19} - 3.1824 \times 10^{-19} = 1.326 \times 10^{-19} \, \text{J} \).

1.2 × 10⁻¹⁹ J
1.3 × 10⁻¹⁹ J
1.326 × 10⁻¹⁹ J
1.4 × 10⁻¹⁹ J
3

The maximum frequency of X-rays produced by a \( 20 \, \text{kV} \) tube is: (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

Energy \( E = e V = 1.6 \times 10^{-19} \times 20 \times 10^3 = 3.2 \times 10^{-15} \, \text{J} \).

\( v_{\max} = \frac{E}{h} = \frac{3.2 \times 10^{-15}}{6.63 \times 10^{-34}} \approx 4.83 \times 10^{18} \, \text{Hz} \).

4.5 × 10¹⁸ Hz
4.83 × 10¹⁸ Hz
5.0 × 10¹⁸ Hz
5.5 × 10¹⁸ Hz
2

The threshold wavelength for a metal is \( 600 \, \text{nm} \). What is its work function in eV? (Take \( h c = 1240 \, \text{eV nm} \))

Work function \( \phi_0 = \frac{h c}{\lambda_0} \).

\( \phi_0 = \frac{1240}{600} \approx 2.07 \, \text{eV} \).

2.07 eV
2.5 eV
3.0 eV
3.5 eV
1

The minimum wavelength of X-rays from a \( 25 \, \text{kV} \) tube is: (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

\( E = e V = 1.6 \times 10^{-19} \times 25 \times 10^3 = 4.0 \times 10^{-15} \, \text{J} \).

\( \lambda_{\min} = \frac{h c}{E} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{4.0 \times 10^{-15}} = 4.9725 \times 10^{-11} \, \text{m} \approx 0.0497 \, \text{nm} \).

0.04 nm
0.045 nm
0.048 nm
0.05 nm
4

The momentum of a photon is \( 2.21 \times 10^{-27} \, \text{kg m/s} \). What is its wavelength? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

For a photon, \( p = \frac{h}{\lambda} \).

\( \lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34}}{2.21 \times 10^{-27}} \approx 3.0 \times 10^{-7} \, \text{m} = 300 \, \text{nm} \).

250 nm
280 nm
300 nm
320 nm
3

Light of wavelength \( 450 \, \text{nm} \) is incident on a metal with work function \( 1.9 \, \text{eV} \). What is the maximum kinetic energy in eV? (Take \( h c = 1240 \, \text{eV nm} \))

\( E = \frac{h c}{\lambda} = \frac{1240}{450} \approx 2.756 \, \text{eV} \).

\( K_{\max} = E - \phi_0 = 2.756 - 1.9 \approx 0.856 \, \text{eV} \).

0.7 eV
0.856 eV
0.9 eV
1.0 eV
2

Which scientist proposed that moving particles of matter exhibit wave-like properties?

Louis de Broglie proposed the wave-particle duality of matter, suggesting that particles like electrons have associated wavelengths (\( \lambda = \frac{h}{p} \)).

Albert Einstein
J.J. Thomson
Max Planck
Louis de Broglie
4

The de Broglie wavelength of an electron is \( 0.2 \, \text{nm} \). What is its speed? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( m_e = 9.11 \times 10^{-31} \, \text{kg} \))

\( p = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34}}{0.2 \times 10^{-9}} = 3.315 \times 10^{-24} \, \text{kg m/s} \).

\( v = \frac{p}{m} = \frac{3.315 \times 10^{-24}}{9.11 \times 10^{-31}} \approx 3.64 \times 10^6 \, \text{m/s} \).

3.0 × 10⁶ m/s
3.5 × 10⁶ m/s
3.64 × 10⁶ m/s
4.0 × 10⁶ m/s
3

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