Dual Nature of Matter and Radiation
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See all →- De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm) Answer: 2. 0.67 nm Key idea: Bohr's quantization 2π r_n=nλ (electron wave fits the orbit). Radius of the n=2 orbit: r₂=n²a₀=4×0.052=0.208 nm... 1
- A photon and an electron (mass m) have the same energy E. The ratio ≤ft(λ_photon/λ_electron) of their de Broglie wavelengths is: (c is the speed of light) Answer: 3. c√(2m/E) Key idea: λ=h/p , with different momentum-energy relations for photon and electron. Photon: E=pc⇒λ_ph=hc/E . Electron: E... 1
- Which of the following options represent the variation of photoelectric current with property of light shown on the x-axis?A. Photoelectric current vs Intensity of light: straight line through origin risingB. Photoelectric current vs Intensity of lig… Answer: 1. A only Key idea: at a fixed frequency above the threshold, the photoelectric current is directly proportional to the intensity. A... 1
- If c is the velocity of light in free space, the correct statements about photon among the following are :A. The energy of a photon is E=h.B. The velocity of a photon is c.C. The momentum of a photon, p=h/c.D. In a photon-electron collision, both tot… Answer: 3. A, B, C and D only Key idea: Go through the properties of a photon. A: E=hν . True. B: Speed is c . True. C: p=hν/c=frac hλ . Tru... 1
- The graph which shows the variation of ≤ft(1/λ^2) and its kinetic energy, E is (where λ is de Broglie wavelength of a free particle) : Answer: 1. graph (1) Key idea: For a free particle E=p²/2m and λ=h/p . So E=h²/2mλ² , which gives frac1λ²=2m/h²E . frac1λ² is directly propo... 1
- The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to: Answer: 3. 1/V The shortest X-ray wavelength occurs when the electron gives all its kinetic energy to one photon: eV=dfrachcλ_min . λ_min=hc... 1