A `20cm` length of a certain solution causes right-handed rotation of `38^@`. A `30cm` length of another solution causes left-handed rotation of `24^@`. The optical rotation caused by `30cm` length of a mixture of the above solutions in the volume ratio `1:2` is

Options

A. (a) Left handed rotation of `14^@`
B. (b) Right handed rotation of `14^@`
C. (c) Left handed rotation of `3^@`
D. (d) Right handed rotation of `3^@`

Answer

D

Explanation

As `thetaproplambda`
Volume ratio `1:2` in a tube of length `30cm` means `10cm` length of first solution and `20cm` length of second solution.
Rotation produced by `10cm` length of first solution
`theta_1=(38^@)/(20)xx10=19^@`
Rotation produced by `20cm` length of second solution
`theta_2=(24^@)/(30)xx20=-16^@`
`:.` Total rotation produced `=19^@-16^@=3^@`