Dual Nature of Matter Chapter-Wise Test 5

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the nature of the relationship between the stopping potential and the frequency of incident light in the photoelectric effect?

The stopping potential \( V_0 \) varies linearly with frequency (\( e V_0 = h v - \phi_0 \)), as shown by experimental graphs and Einstein’s equation.

Inverse
Exponential
Quadratic
Linear
4

The threshold frequency of a metal is \( 3.0 \times 10^{14} \, \text{Hz} \). What is the maximum kinetic energy of electrons emitted by light of wavelength \( 500 \, \text{nm} \)? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \))

\( \phi_0 = h v_0 = 6.63 \times 10^{-34} \times 3.0 \times 10^{14} = 1.989 \times 10^{-19} \, \text{J} \).

\( E = \frac{h c}{\lambda} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{500 \times 10^{-9}} = 3.978 \times 10^{-19} \, \text{J} \).

\( K_{\max} = E - \phi_0 = 3.978 \times 10^{-19} - 1.989 \times 10^{-19} = 1.989 \times 10^{-19} \, \text{J} \).

1.5 × 10⁻¹⁹ J
1.8 × 10⁻¹⁹ J
1.989 × 10⁻¹⁹ J
2.0 × 10⁻¹⁹ J
3

What characteristic of light quanta (photons) is directly proportional to their frequency?

The energy of a photon is given by \( E = h v \), making it directly proportional to frequency.

Wavelength
Energy
Intensity
Speed
2

A photon has a momentum of \( 1.8 \times 10^{-27} \, \text{kg m/s} \). What is its wavelength? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

\( \lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34}}{1.8 \times 10^{-27}} \approx 3.683 \times 10^{-7} \, \text{m} = 368.3 \, \text{nm} \).

350 nm
360 nm
368 nm
370 nm
3

Light of wavelength \( 400 \, \text{nm} \) is incident on a metal with a stopping potential of \( 1.2 \, \text{V} \). What is the threshold wavelength? (Take \( h c = 1240 \, \text{eV nm} \))

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

\( K_{\max} = e V_0 = 1.2 \, \text{eV} \).

\( \phi_0 = E - K_{\max} = 3.1 - 1.2 = 1.9 \, \text{eV} \).

\( \lambda_0 = \frac{h c}{\phi_0} = \frac{1240}{1.9} \approx 652.63 \, \text{nm} \).

600 nm
620 nm
653 nm
700 nm
3

Which property of incident light determines the maximum kinetic energy of photoelectrons, assuming the metal remains the same?

According to Einstein’s photoelectric equation, \( K_{\max} = h v - \phi_0 \), the maximum kinetic energy depends on the frequency of the incident light.

Frequency
Intensity
Wavelength
Polarization
1

A light source emits photons of energy \( 4.5 \times 10^{-19} \, \text{J} \) at a rate of \( 2.0 \times 10^{16} \) photons per second. What is the wavelength of the light? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \))

\( \lambda = \frac{h c}{E} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{4.5 \times 10^{-19}} = 4.42 \times 10^{-7} \, \text{m} = 442 \, \text{nm} \).

400 nm
420 nm
430 nm
442 nm
4

A photon of wavelength \( 300 \, \text{nm} \) is incident on a metal. What is its energy in eV? (Take \( h c = 1240 \, \text{eV nm} \))

Energy \( E = \frac{h c}{\lambda} \).

\( E = \frac{1240}{300} \approx 4.13 \, \text{eV} \).

4.13 eV
4.0 eV
3.8 eV
3.5 eV
1

Light of frequency \( 6.2 \times 10^{14} \, \text{Hz} \) is incident on a metal with work function \( 2.1 \, \text{eV} \). What is the stopping potential? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

\( E = h v = 6.63 \times 10^{-34} \times 6.2 \times 10^{14} = 4.1106 \times 10^{-19} \, \text{J} \).

\( E = \frac{4.1106 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 2.569 \, \text{eV} \).

\( K_{\max} = E - \phi_0 = 2.569 - 2.1 = 0.469 \, \text{eV} \).

\( V_0 = \frac{K_{\max}}{e} = 0.469 \, \text{V} \).

0.4 V
0.45 V
0.5 V
0.47 V
4

Which of the following particles was historically identified as a universal constituent of matter through cathode ray experiments?

J.J. Thomson’s experiments with cathode rays led to the discovery of electrons as fundamental negatively charged particles in matter.

Electron
Proton
Neutron
Photon
1

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