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For ideal light emitting diodes (LEDs) fabricated from various semiconductor materials, a graph is plotted with the wavelength of the emitted light ( ) on the y-axis and the reciprocal of the bandgap energy ( 1 E_g ) on the x-axis, where E_g is measured in Joules. What will be the shape of this graph and the value of its slope?

Options

  1. ARectangular hyperbola
  2. BStraight line passing through the origin with slope h c
  3. CStraight line passing through the origin with slope hc e
  4. DStraight line passing through the origin with slope hc

Correct answer

D. Straight line passing through the origin with slope hc

Step-by-step solution

The energy of the emitted photon is approximately equal to the bandgap energy of the semiconductor, given by the relation: E_g = hc Rearranging this equation to express wavelength as a function of the reciprocal of the bandgap energy gives: = hc ( 1 E_g ) Comparing this with the standard equation of a straight line passing through the origin, y = mx , we identify: y = x = 1 E_g Therefore, the graph of versus 1 E_g is a straight line passing through the origin. The slope of this line ( m ) corresponds to the product

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