if rahe radius of the first Bohr orbit is x, then find the de Broglie wavelength of electron in third orbit.

Explanation

The radius of the n-th orbit `r_(n) prop n^(2)`
`therefore (r_(1))/(r_(3))=(n_(1)^(2))/(n_(3)^(2))=(1^(2))/(3^(2))=(1)/(9)`
`therefore r_(3)=9xxr_(1)=9x" "[because r_(1)=x]`
Now, circumference of the n-th orbit is an integral multiple of the wavelength associated with the motion of the electron i.e.,
`2pir_(n)=nxxlamda`
`therefore 2pir_(30=3xxlamda`
or, `lamda=(2pir_(3))/(3)=(2pi)/(3)xx9x=6pix`