(a) construct an expression for a quantity having the dimension of length starting from velocity of light c, the mass of an electron m and Planck's constant h.
(b) Evaluate the value of this length taking constant of proportionality to be unity, `m=9.1xx10^(-31) kg, c=3xx10^(8) m//s` and `h=6.63xx10^(-34) J-s`.
[This wavelength is called Compton wavelength and plays an important role in atomic physics.]

Answer

(a) `lambda_(c)=(h//mc)`
(b) `lambda_(c)=2.43xx10^(-12) m`

Explanation

`[L]=[LT^(-1)]^(x)[M]^(y)[ML^(2)T^(-1)]^(z)`
`x=-1`
`z=1`
`y=-1`
`lambda_(c)=h/(mc)`