Dual Nature of Matter And Radiation Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A photon has a momentum of \( 2.0 \times 10^{-27} \, \text{kg m/s} \). What is its energy in joules? (Take \( c = 3 \times 10^8 \, \text{m/s} \))

For a photon, \( p = \frac{E}{c} \).

\( E = p c = 2.0 \times 10^{-27} \times 3 \times 10^8 = 6.0 \times 10^{-19} \, \text{J} \).

5.5 × 10⁻¹⁹ J
5.8 × 10⁻¹⁹ J
6.0 × 10⁻¹⁹ J
6.5 × 10⁻¹⁹ J
3

Light of wavelength \( 400 \, \text{nm} \) produces photoelectrons with a stopping potential of \( 0.8 \, \text{V} \) from a metal. What is the work function of the metal in eV? (Take \( h c = 1240 \, \text{eV nm} \))

Photon energy \( E = \frac{h c}{\lambda} = \frac{1240}{400} = 3.1 \, \text{eV} \).

\( K_{\max} = e V_0 = 0.8 \, \text{eV} \).

\( \phi_0 = E - K_{\max} = 3.1 - 0.8 = 2.3 \, \text{eV} \).

2.0 eV
2.1 eV
2.3 eV
2.5 eV
2

A particle of mass \( 1.5 \times 10^{-30} \, \text{kg} \) has the same momentum as a photon of wavelength \( 500 \, \text{nm} \). What is its speed? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

Photon momentum \( p = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34}}{500 \times 10^{-9}} = 1.326 \times 10^{-27} \, \text{kg m/s} \).

\( v = \frac{p}{m} = \frac{1.326 \times 10^{-27}}{1.5 \times 10^{-30}} = 8.84 \times 10^2 = 884 \, \text{m/s} \).

800 m/s
850 m/s
870 m/s
884 m/s
4

A photon has a wavelength of \( 200 \, \text{nm} \). What is its momentum? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

\( p = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34}}{200 \times 10^{-9}} = 3.315 \times 10^{-27} \, \text{kg m/s} \).

3.0 × 10⁻²⁷ kg m/s
3.2 × 10⁻²⁷ kg m/s
3.315 × 10⁻²⁷ kg m/s
3.5 × 10⁻²⁷ kg m/s
3

The threshold wavelength of a metal is \( 620 \, \text{nm} \). What is the work function in eV? (Take \( h c = 1240 \, \text{eV nm} \))

\( \phi_0 = \frac{h c}{\lambda_0} = \frac{1240}{620} = 2.0 \, \text{eV} \).

1.8 eV
2.0 eV
2.2 eV
2.5 eV
2

A photon has a wavelength of \( 250 \, \text{nm} \). What is its energy in joules? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \))

\( E = \frac{h c}{\lambda} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{250 \times 10^{-9}} = 7.974 \times 10^{-19} \, \text{J} \).

7.974 × 10⁻¹⁹ J
7.5 × 10⁻¹⁹ J
8.0 × 10⁻¹⁹ J
8.5 × 10⁻¹⁹ J
1

The work function of a metal is \( 1.5 \, \text{eV} \). Light of wavelength \( 400 \, \text{nm} \) is incident on it. What is the maximum kinetic energy of emitted electrons in eV? (Take \( h c = 1240 \, \text{eV nm} \))

\( E = \frac{h c}{\lambda} = \frac{1240}{400} = 3.1 \, \text{eV} \).

\( K_{\max} = E - \phi_0 = 3.1 - 1.5 = 1.6 \, \text{eV} \).

1.4 eV
1.6 eV
1.8 eV
2.0 eV
2

An electron moves with a speed of \( 3.0 \times 10^6 \, \text{m/s} \). What is its de Broglie wavelength? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( m_e = 9.11 \times 10^{-31} \, \text{kg} \))

Momentum \( p = m v = 9.11 \times 10^{-31} \times 3.0 \times 10^6 = 2.733 \times 10^{-24} \, \text{kg m/s} \).

\( \lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34}}{2.733 \times 10^{-24}} \approx 2.425 \times 10^{-10} \, \text{m} = 0.2425 \, \text{nm} \).

0.2425 nm
0.25 nm
0.3 nm
0.35 nm
1

A photon of frequency \( 8.0 \times 10^{14} \, \text{Hz} \) has what energy in joules? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

\( E = h v = 6.63 \times 10^{-34} \times 8.0 \times 10^{14} = 5.304 \times 10^{-19} \, \text{J} \).

5.304 × 10⁻¹⁹ J
5.0 × 10⁻¹⁹ J
5.5 × 10⁻¹⁹ J
6.0 × 10⁻¹⁹ J
1

The maximum speed of photoelectrons emitted from a surface is \( 5.0 \times 10^5 \, \text{m/s} \). What is the stopping potential? (Take \( m_e = 9.11 \times 10^{-31} \, \text{kg} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

\( K_{\max} = \frac{1}{2} m v_{\max}^2 = \frac{1}{2} \times 9.11 \times 10^{-31} \times (5.0 \times 10^5)^2 = 1.13875 \times 10^{-19} \, \text{J} \).

\( V_0 = \frac{K_{\max}}{e} = \frac{1.13875 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 0.71 \, \text{V} \).

0.6 V
0.71 V
0.8 V
0.9 V
2

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