**WAVE- PARTICLE PARADOX**

**(A)Wave nature of matter**

Can be expressed as *∆= h/mv*

*Where h is the Planck constant, m is the mass, v is the velocity, ∆ is the wavelength.*

**WAVE PARTICLE DUALITY **

The study of the behavior of light and other Electromagnetic radiation including interference and diffraction demonstrate the wave nature of light. Others, such as the photo-electric effect, Compton scattering phenomenon point to the particle nature of light. The two theories seem to be incompatible but both have been shown to be valid. This is the wavelength duality.

**THE HEISENBERG’S UNCERTAINTY PRINCIPLE**

*The uncertainty principle states that neither the position nor the momentum of a particle can be determined with great precision simultaneously. ∆E= uncertainty of energy, ∆t= uncertainty of time interval, h= Planck constant. * *∆E∆t **>** h/2π **( this is Heisenberg’s uncertainty principle for energy and time interval.*

**QUESTIONS**

1.Calculate the wavelength of

(I) an electron moving with a Velocity of 2.3×10^{6}ms^{-1}

(II) a ball of mass 0.2kg moving with a speed of 20ms^{-1}.

**Solution:** ∆= h/mv

∆= 6.63×10^{-34}/ 9.1×10^{-13}×2.3×10^{6}

= 3.2×10^{-10}m

= 3.2A°(1A=Armstrong unit =10^{-10}m)

(II)∆_{b} = 6.63×10^{-13}^{ } = 1.66×10^{-34}m.

=0.2×20

2..State Heisenberg’s uncertainty principle of position and momentum.

**Solution:** the uncertainty principle states that neither the position nor the momentum of a particle can be determined with great precision simultaneously.

3.determine the uncertainty in the:

(I) energy of a photon which is radiated in a time interval 10^{-5}s

(II) momentum of a 0.2kg football moving with a speed of 20ms^{-1} and restricted to a region of 25cm. Determine the fractional uncertainty in momentum.

**Solution:**

∆E.∆t > h/2π

∆E > 6.63×10^{-34}/2×π×10^{-5}

> 1.06×10^{-29}J

(II) ∆p.∆x > h/2π = 6.63×10^{-34}/2π

∆p_{x} = 6.63×10^{-34 }/2π.∆x. = 6.63×10^{-34}/2×π×25×10^{-2}

=4.2×10^{-34}

Fractional uncertainty,

∆p_{x/ Px. }= 4.2×10^{-34} = 1.05×10^{-34}/4

4. Which of the following phenomena supports the theory that waves have a particle nature. (WASSCE 2013)

A. Electron diffraction

B. Photoelectric effect

C. Diffraction of light

D. X-ray interference

**Answer:** C

5. (b) state one phenomenon that can only be explained in terms of the wave nature of light. (WASSCE 2008 theory)

**Answer: **photo-electric effect

6. There is always an uncertainty involved in any attempt to measure the position and momentum of an electron simultaneously. This statement is known as the? (WASSCE 2007)

A. De Broglie’s law

B. Heisenberg’s uncertainty principle

C. Franck- Hertz experimental law

D. Wave- particle paradox

**Answer:** B

7. Which of the following is correct about Photoelectric effects? (Jamb 1987)

A. It cannot occur in liquids

B. The energy of the emitted electron is independent of the work function of the surface

C. The energy of the emitted electron depends on the wavelength of the incident light

D. The greater the intensity of the incident light, the greater the energy of the emitted electron

**Answer: **C

8. Which of the following statements is a correct consequence of the wave-particle duality?

A. Electrons can behave like waves and particles

B. Light behaves as waves only

C. Electrons behave like particles only

D. Photons behave like waves

**Answer:** A

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