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The wavalenght (lambda) of matter waves ...

The wavalenght `(lambda)` of matter waves may depends upon Planck's constant (h) mass (m) and velocity `(upsilon)` of the particle. Use the method of dimensions to derive the formula

Text Solution

Verified by Experts

The correct Answer is:
`lambda = (kh)/(m upsilon)`
`lambda = kh^a =m^b upsilon^c`
`[M^0 L^1 T^00] = [ML^2 L^(-1)]^a M^b [LT^(-1)]^c`
`= M^(a+b)L^(2a +c) T^(-a -c)`
Applying principle of homogeneity of
dimensions, we get
a +b =0 ….(i)
2a + c =1 …..(ii)
- a -c =0. ….(iii)
Add (ii) & 9iii) a =1
From (i) b = -a = -1
From (iii), c = -a=-1
`:. [lambda= (kh)/(mupsilon)`]
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Knowledge Check

  • The velocity of water wave v may depend on their wavelength lambda , the density of water rho and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

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    B
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    C
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