NEETPhysicsDual Nature of Matter
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
- ARectangular hyperbola
- BStraight line passing through the origin with slope h c
- CStraight line passing through the origin with slope hc e
- 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