The dimensional formula for Planck's constant and angular momentum are

Options

A. `[ML ^(2) T ^(-2)] and [MLT ^(-1) ]`
B. `[ML ^(2) T ^(-1) ] and [ML ^(2) T ^(-1)]`
C. `[ML ^(3) T ^(1) ] and [MLT ^(-2)]`
D. `[MLT^(-1) ] and [MLT^(-2)]`

Answer

B

Explanation

Angular momentum of a particle moving in circular path about centre is
`L _(0) = mvR`
By principle of homogeneity
`[L _(0) ] = [mv R] = M ^(1) xx L ^(1) T^(-1)xx L ^(1) `
i.e. `[L _(0) ] = M ^(1) L ^(2) T ^(-1)`
Now, according quatization of bohr orbits, angular momentum of an electron is given as `L _(0) = ( nh)/(2pi)` By principle of homogeneity
`[L _(0) ] =[h]`
Because `(n)/(2pi)` is dimensionless.