Consider Bohr's theory for hydrogen atom . The magnitude of orbit angular momentum orbit radius and velocity of the electron in nth energy state in a hydrogen atom are l , r and v respectively. Find out the value of 'x' if product of v, r and l (vrl) is directly proportional to `n^(x)`.

Answer

`x=2`

Explanation

`{:("Angular momentum,"l=mvr=(nh)/(2pi),:.,l prop n,,),("Radius,"r=0.529 n^(2)/zÅ,:.,r prop n^(2),"For same Z",),("Velocity,"v=2.18xx10^(6) z/n m//s,:.,v prop 1/n,,):}`
`:. v r l propnxxn^(2)xx1/n`
But, `v r l prop n^(x)` (given)
`:. n^(2)=n^(x)`
`:. x=2`