Explain the wave-particle duality of light. (b) A particle of wavelength 4.2x 10\(^{-11}\)m travels (a) With a momentum of 1.6 x 10\(^{-23}\) kg m/s, Determ...

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(a) Wave-particle duality of light. Light shows a dual nature. In some experiments it behaves as a wave (it undergoes interference, diffraction and polarisation, as in Young's double-slit experiment), while in other experiments it behaves as a stream of particles called photons, each carrying energy \(E=hf\) (as in the photoelectric effect and the Compton effect). Light is therefore neither purely a wave nor purely a particle; it exhibits whichever behaviour the experiment probes. The two aspects are linked by the de Broglie relation \(\lambda = h/p\).

(b) Finding Planck's constant. The de Broglie relation connects wavelength and momentum:

\[ \lambda = \frac{h}{p} \quad\Rightarrow\quad h = \lambda p \]

With \(\lambda = 4.2\times10^{-11}\ \text{m}\) and \(p = 1.6\times10^{-23}\ \text{kg m/s}\):

\[ h = (4.2\times10^{-11})(1.6\times10^{-23}) \] \[ h = 6.72\times10^{-34}\ \text{J s} \]

Planck's constant is about \(6.72\times10^{-34}\ \text{J s}\), in good agreement with the accepted value \(6.63\times10^{-34}\ \text{J s}\).