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The variation of de-Broglie wavelength with 1 K (where K is the kinetic energy) is plotted for a deuteron and an alpha particle. The graphs are straight lines passing through the origin. The ratio of the slopes of the lines for the deuteron and the alpha particle is

Options

  1. A1:2
  2. B2:1
  3. C1: 2
  4. D2 :1

Correct answer

D. 2 :1

Step-by-step solution

The de-Broglie wavelength is given by = h 2mK . This can be written as = ( h 2m ) 1 K . The slope of the versus 1 K graph is S = h 2m . Therefore, the slope is inversely proportional to the square root of the mass of the particle, i.e., S 1 m . For a deuteron, mass m_d = 2u . For an alpha particle, mass m_ = 4u . The ratio of their slopes is S_d S_ = m_ m_d = 4u 2u = 2 . Thus, the ratio is 2 :1 . Answer: 2 :1

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