2. Explain the meaning and consequences for chemistry of wave-particle duality.

Question

2. Explain the meaning and consequences for chemistry of wave-particle duality. (4 Marks)

3. Calculate the de Broglie wavelength of (a) a mass of 1.0 g travelling at 1.0 m s1 , and (b) an He atom travelling at 1000 m s1 (a typical speed at room temperatures). (2 Marks)

4. Calculate the energy of the first three bands in the Lyman series of the atomic spectra of the hydrogen atom. (3 Marks)

5. Calculate the minimum uncertainty in (a) the speed of a ball of mass 500 g that is known to be within 1.0 µm of a certain point on a bat, and (b) What is the minimum uncertainty in the position of a bullet of mass 5.0 g that is known to have a speed somewhere between 350.000 01 m s1 and 350.000 00 m s1 ?

Explanation / Answer

2.

de Broglie suggested that matter can exhibit dual behavior i.e., both particle nature and wave nature. He gave; = /mv = /p.

Where, is the wavelength

h is the planks constant, = 6.626 x 10-34 Joule Second

m is the mass

v is the velocity

p is the momentum

3.

m = 1g

v = 1 m/s

= /mv = 6.626 x 10-34 / 1 x 1 = 6.626 x 10-34 Js

mass of He atom = 4 g and v given as 1000 m/s

= /mv = (6.626 x 10-34 ) / (4 x 1000)

= 1.6565x10-37

5.

Heisenberg uncertainty principle

x. v /4m

a) calculate uncertainty in velocity, v = h/4m x

= (6.626 x 10-34 ) / 4 x 3.14 x 500 x 1

= 1.05456 x 10-37

b) calculate uncertainty in position, x = h/4m v

=(6.626 x 10-34 ) / (4 x 3.14 x 5 g x (350.00001-350.00000)

= (6.626 x 10-34 ) / (4 x 3.14 x 5 g x 10-5)

= 1.05456x10-30

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