Assertion: The kinetic energy of the photoelectrons is directly proportional to the intensity of incident light.
Reason: The rate of emission of photoelectrons is inversely proportional to the intensity of incident light.
Assertion: Angular momentum of an electron in any orbit is given by angular momentum [tex]=\frac{n \cdot h}{2 \pi}[/tex], where [tex]n[/tex] is the principal quantum number.
Reason: The principal quantum number, [tex]n[/tex], can have any integral value.
Answer (2)
The first assertion is false as kinetic energy of photoelectrons depends on the frequency of light, not the intensity. The second assertion is true; angular momentum follows the relationship L = 2 π n ⋅ h , and the reason regarding the principal quantum number is partially correct since it must be a positive integer.
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Assertion 1 is false because kinetic energy depends on the frequency of light, not intensity.
Reason 1 is false because the rate of emission is directly proportional to the intensity.
Assertion 2 is true; angular momentum is quantized as L = 2 π nh .
Reason 2 is partially correct; n must be a positive integer, so the final answer is Assertion 1 is false, Reason 1 is false, Assertion 2 is true, and Reason 2 is partially correct.
Explanation
Analyzing the Photoelectric Effect Let's analyze the first assertion and reason regarding the photoelectric effect.
Evaluating Assertion 1 The assertion states that the kinetic energy of photoelectrons is directly proportional to the intensity of incident light. This is incorrect. According to the photoelectric effect, the kinetic energy of photoelectrons depends on the frequency of the incident light, not the intensity. The equation is given by K E ma x = h f − o b re ak \[ 0.1 c m ] ϕ , where K E ma x is the maximum kinetic energy, h is Planck's constant, f is the frequency, and ϕ is the work function.
Evaluating Reason 1 The reason states that the rate of emission of photoelectrons is inversely proportional to the intensity of incident light. This is also incorrect. The rate of emission of photoelectrons is directly proportional to the intensity of incident light. Higher intensity means more photons, leading to more photoelectrons being emitted.
Analyzing Bohr's Model Now let's analyze the second assertion and reason regarding Bohr's model and angular momentum.
Evaluating Assertion 2 The assertion states that the angular momentum of an electron in any orbit is given by L = 2 π n ". h , where n is the principal quantum number. This is correct. According to Bohr's model, the angular momentum is quantized and given by L = n ℏ = 2 π nh , where n is an integer.
Evaluating Reason 2 The reason states that the principal quantum number, n , can have any integral value. This is not entirely correct. The principal quantum number, n , can have any positive integral value (1, 2, 3, ...), but it cannot be zero or negative.
Conclusion In summary:
Assertion 1 is false.
Reason 1 is false.
Assertion 2 is true.
Reason 2 is not entirely correct, as n must be a positive integer.
Examples
Understanding the photoelectric effect and Bohr's model is crucial in various applications, such as designing solar cells and understanding atomic spectra. For instance, the photoelectric effect explains how solar cells convert light into electricity, while Bohr's model helps predict the wavelengths of light emitted by different elements. These concepts are fundamental in fields like renewable energy and spectroscopy, enabling advancements in technology and scientific research.
