Emotional Development
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Consider the following statements regarding modern physics and atomic structure:
- 1. According to Einstein's photoelectric equation ($K_{max} = h\nu - \Phi$), the maximum kinetic energy of emitted photoelectrons depends linearly on the frequency of incident light and is independent of the intensity of light.
- 2. According to Bohr's atomic model, the angular momentum ($L$) of an electron in any stable orbit of a hydrogen atom is an integral multiple of Planck's constant ($h$), i.e., $L = \frac{nh}{2\pi}$, where $n$ is the principal quantum number.
- 3. According to the law of radioactive decay, the rate of disintegration of any radioactive substance at any instant is inversely proportional to the total number of atoms present at that time, and its half-life period is directly proportional to the square of the decay constant.
- 4. According to the mass-energy equivalence principle ($E = mc^2$), in both nuclear fusion and nuclear fission processes, mass defect is converted into energy due to an increase in binding energy per nucleon.
Which of the above statement(s) is/are completely true?
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Detailed Explanation
Statement 1 is true because photoelectric kinetic energy depends on frequency, not intensity. Statement 2 is true as it represents Bohr's quantization condition. Statement 3 is false because the rate of radioactive decay is directly proportional to the number of atoms present ($-\frac{dN}{dt} = \lambda N$), and half-life is inversely proportional to the decay constant. Statement 4 is true as mass defect converts to energy in nuclear reactions.
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