Question

The wavelength (2) of matter waves may depend upon Planck's constant (h), mass (m) and velocity (v) of the particle. Use the method of dimensions to derive the formula

Answer 1

Answer:

Wavelength dimension =[L]

Mass Dimension =[M]

Velocity dimension =[LT

−1

]

Planck constant dimension =[ML

2

T

−1

]

now,

[L]=K[M]

a

[LT

−1

]

b

[ML

2

T

−1

]

c

=K[M]

(a+c)

[L]

(b+2c)

[T]

(b−c)

Compare L.H.S to R.H.S

at c=0 ; b+2c=1 ; −b−c=0

c=1 ; b=−1 ; a=−1