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Match the following ratio of De-Broglie wavelengths of a proton and ( ) particle, when both ( array |l|l|l|l| & List-I & & List-II A & Have same speed & (p) & 2: 1 B & array l Have same potential difference array & (q) & 1: 1 C & array l Have same kinetic energy. array & (r) & 4: 1 D & array l Have same linear momentum array & (s) & 2 2 : 1 array )

Options

  1. A( array |c|c|c|c|c| & A & ~B & C & D 1 & p & q & r & ~s array )
  2. B( array |c|c|c|c|c| & A & ~B & C & D 2 & r & ~s & p & q array )
  3. C( array |c|c|c|c|c| & A & ~B & C & D 3 & p & r & q & ~s array )
  4. D( array |c|c|c|c|c| & A & ~B & C & D 4 & r & q & ~s & p array )

Correct answer

B. ( array |c|c|c|c|c| & A & ~B & C & D 2 & r & ~s & p & q array )

Step-by-step solution

Here's the detailed matching: - A. Have the same speed (List-II: r) For the same speed, the de Broglie wavelength ( ) is inversely proportional to mass ( ( 1 m ) ). Since the mass of a proton is about half that of an a-particle (which has twice the mass of a proton), the ratio of de Broglie wavelengths will be ( _p: _ =2: 1 ). - B. Have the same potential difference (List-II: s) For the same potential difference, the kinetic energy gained by the particles is proportional to their charge. Since the a-particle has tw

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