Consider the two following statements I and II, and identify the correct choice given in the answers
1. In photovoltaic cells, the photoelectric current produced is not proportional to the intensity of incident light.
2. In gas-filled photoemissive cells, the velocity of photoelectrons depends on the wavelength of the incident radiation.

Options

A. Both 1 and 2 are true
B. Both 1 and 2 are false
C. 1 is true but 2 is false
D. 1 is false but 2 is true

Answer

To solve the problem, we need to analyze the two statements given and determine their validity.

**Statement I:** "In photovoltaic cells, the photoelectric current produced is not proportional to the intensity of incident light."

**Step 1:** Understand the concept of photovoltaic cells.
- Photovoltaic cells convert light energy into electrical energy through the photoelectric effect.

**Step 2:** Analyze the relationship between photoelectric current and light intensity.
- Experimental observations show that the photoelectric current produced in photovoltaic cells is directly proportional to the intensity of the incident light, provided the frequency of the light is above a certain threshold.

**Conclusion for Statement I:**
- Since the photoelectric current is indeed proportional to the intensity of the incident light, Statement I is **false**.

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**Statement II:** "In gas-filled photoemissive cells, the velocity of photoelectrons depends on the wavelength of the incident radiation."

**Step 3:** Understand gas-filled photoemissive cells.
- In these cells, photons of light incident on a gas can eject electrons from the gas atoms.

**Step 4:** Analyze the relationship between the velocity of photoelectrons and the wavelength of the incident radiation.
- The energy of the incident photon can be expressed as \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
- The kinetic energy of the emitted photoelectron can be described by the equation:
\[ KE = \frac{1}{2}mv^2 = \frac{hc}{\lambda} - \phi \]
where \( \phi \) is the work function of the gas.

**Step 5:** Determine how the velocity of the photoelectron is affected.
- From the above equation, we can see that the velocity \( v \) of the photoelectron depends on the wavelength \( \lambda \) of the incident radiation. As the wavelength changes, the energy of the photon changes, which in turn affects the kinetic energy and thus the velocity of the emitted electrons.

**Conclusion for Statement II:**
- Since the velocity of photoelectrons does depend on the wavelength of the incident radiation, Statement II is **true**.

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**Final Conclusion:**
- Statement I is false, and Statement II is true.

**Correct Choice:**
- The correct answer is that Statement I is false and Statement II is true.

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